Algebra and Trigonometry (4th Edition)

Chapter 11

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The component form of a vector in a plane with ... more

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The component form of a vector in a plane with ... more

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The component form of a vector in a plane with ... more

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The component form of a vector in a plane with ... more

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The component form of a vector in a plane with ... more

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The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; The component form of a vector in a plane with ... more

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; For a vector defined by its initial point at ... more

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; For a vector defined by its initial point at ... more

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; For a vector defined by its initial point at ... more

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; For a vector defined by its initial point at ... more

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For a vector defined by its initial point at and... more

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For a vector defined by its initial point at and... more

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For a vector defined by its initial point at and... more

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For a vector defined by its initial point at and... more

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; The vector can be represented by unit vectors... more

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; The vector can be represented by unit vectors... more

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; The vector can be represented by unit vectors... more

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; The vector can be represented by unit vectors... more

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, , , ; Given the vector , , where is a scalar... more

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, , , ; Given the vector , , where is a scalar... more

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, , , ; Given the vector , , where is a scalar... more

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, , , ; Given the vector , , where is a scalar... more

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, , , ; Given the vector , , where is a scalar... more

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, , , ; Given the vector , , where is a scalar... more

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, , , , , , ; Find the magnitude of , by applying ... more

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, , , , , , ; Find the magnitude of , by applying ... more

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, , , , , , ; Find the magnitude of , by applying ... more

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, , , , , , ; Find the magnitude of , by applying ... more

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, , ; For a vector , the horizontal and vertical ... more

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, , ; For a vector , the horizontal and vertical ... more

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, , ; For a vector , the horizontal and vertical ... more

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, , ; For a vector , the horizontal and vertical ... more

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, , ; For a vector , the horizontal and vertical ... more

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, , ; For a vector , the horizontal and vertical ... more

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, ; A vector can be expressed using its magnitude... more

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, ; A vector can be expressed using its magnitude... more

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, ; A vector can be expressed using its magnitude... more

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, ; A vector can be expressed using its magnitude... more

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, ; A vector can be expressed using its magnitude... more

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, ; A vector can be expressed using its magnitude... more

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, ; Draw the vector in standard position. That is... more

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, ; Draw the vector in standard position in the -... more

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; Draw the vectors and in standard positions in... more

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; Given the initial and final positions of the ... more

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; Given the initial and final positions of the ... more

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; Draw the vectors , and in standard positions ... more

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, ; Draw the vectors , and in standard positions... more

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; Given that the initial and final positions of ... more

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; Given that the initial and final positions of ... more

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or , ; To find the magnitude of the resultant ... more

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, ; Since the system is under mechanical ... more

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, ; Since the system is under mechanical ... more

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The sum of the vectors drawn from head to tail, ... more

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; Given the two vectors and , the dot product , ... more

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; Given the two vectors and , the dot product ... more

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; If a constant force is applied to an object, ... more

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The two vectors will be perpendicular if their dot... more

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The two vectors will be perpendicular if their dot... more

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The two vectors will be perpendicular if their dot... more

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The two vectors will be perpendicular if their dot... more

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The two vectors will be perpendicular if their dot... more

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The two vectors will be perpendicular if their dot... more

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9 ; Find using the formula , where and are the ... more

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9 ; Add and .  ; Calculate the dot product of ... more

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; Add the vectors and . ; Subtract the vectors ... more

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; Calculate the dot product of the vectors and... more

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; Find the dot product of and using the formula... more

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; Find the dot product of and using the formula... more

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-24 ; Find the dot product of and using the ... more

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; Find the dot product of and using the formula... more

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; Calculate the displacement vector.  ; To ... more

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; Calculate the displacement vector.  ; To ... more

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; Calculate the displacement vector.  ; To ... more

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; Calculate the displacement vector.  ; To ... more

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Let and and calculate the dot product of the ... more

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Calculate the dot product of and .Calculate the ... more

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Let , and .Calculate .Calculate the dot product ... more

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Let and .Calculate the dot product of and .... more

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Calculate the dot product of and .   Since the ... more

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; Projection of onto is given by: . ; Take the ... more

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; The object moves 4 ft along the x-axis in the ... more

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; Calculate the displacement vector by ... more

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; Work done is given by the dot product of the ... more

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; The work done is given by the product of the ... more

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; Let the force required to keep the car from ... more

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; Let the force required to keep the package from... more

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; Let the component of force along the inclined ... more

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; The three mutually perpendicular axes are ... more

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; The distance between the two points with ... more

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The surface represents a vertical plane which is ... more

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The surface represents a vertical plane which is ... more

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The surface represents a horizontal plane which ... more

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The surface represents a vertical plane which is ... more

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; The standard equation of the sphere is: ; where... more

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; The standard equation of the sphere is: ; where... more

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; The standard equation of the sphere is: ; where... more

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; The standard equation of the sphere is: ; where... more

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Group terms with the same variables.  Complete the... more

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Group the terms with the same variables.   ... more

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Write the similar terms together in the given ... more

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Group the terms with the same variables.   ... more

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3 ; Let the center coordinates of the sphere be . ... more

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Consider a point . Let be the distance between ... more

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Consider a point . Let be the distance between ... more

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unit; ; The vector is equivalent to . ; The ... more

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;  The angle between the vectors and is given ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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3 ; Use the formula to determine the magnitude of... more

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13 ; Use the formula to determine the magnitude ... more

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; Use the formula to determine the magnitude of ... more

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; Use the formula to determine the magnitude of ... more

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, , ; Consider the given vectors and . Add the ... more

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, , ; Consider the given vectors and . Add the ... more

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, , ; Consider the given vectors and . Add the ... more

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, , ; Consider the given vectors and . Add the ... more

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; The vector can be written as in terms of unit... more

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; The vector can be written as in terms of the ... more

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; The vector can be written as in terms of the ... more

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; The vector can be written as in terms of the ... more

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; Find using the formula where , , and are the... more

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; Find using the formula where , , and are the... more

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1 ; Find using the formula where , , and are ... more

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; Find using the formula where , , and are the... more

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Yes. ; The two vectors would be perpendicular if ... more

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No. ; The two vectors would be perpendicular if ... more

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No. ; The two vectors would be perpendicular if ... more

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Yes. ; The two vectors would be perpendicular if ... more

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; To find the value of the angle between and :... more

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; To find the value of the angle between and :... more

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; To find the value of the angle between and :... more

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; To find the value of the angle between and :... more

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, , and ; To find the direction angles of a vector... more

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, , and ; To find the direction angles of the ... more

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, , and ; To find the direction angles of a vector... more

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, , and ; To find the direction angles of a vector... more

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; To find the third direction angle of a vector:... more

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; To find the third direction angle of a vector:... more

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; To find the third direction angle of a vector:... more

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; To find the third direction angle of a vector:... more

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Substitute and into the formula and solve for ... more

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Substitute and into the formula and solve for ... more

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; The cross product of the vectors and is given... more

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Perpendicular ; According to the cross product ... more

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; To find the cross product of the given vectors... more

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; To find the cross product of the given vectors... more

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0 ; To find the cross product of the given vectors... more

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0 ; To find the cross product of the given vectors... more

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; To find the cross product of the given vectors... more

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; To find the cross product of the given vectors... more

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; Find the length of the cross product of the ... more

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10 ; Find the length of the cross product of the ... more

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100 ; Find the length of the cross product of the ... more

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; Find the length of the cross product of the ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The area of the parallelogram spanned by and... more

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; The area of the parallelogram spanned by and... more

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; The area of the parallelogram spanned by and... more

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; The area of the parallelogram spanned by and... more

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; The area of the triangle  spanned by the ... more

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; The area of the triangle  spanned by the ... more

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; The area of the triangle  spanned by the ... more

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; The area of the triangle  spanned by the ... more

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parametric ; The parametric equations of a line ... more

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; The equation of the plane containing the point... more

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; ; ; The parametric equations of a line passing ... more

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; ; ; The parametric equations of a line passing ... more

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; ; ; The parametric equations of a line passing ... more

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; ; ; The parametric equations of a line passing ... more

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; ; ; The parametric equations of a line passing ... more

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; The parametric equations of a line passing ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; The vector in a plane with initial point and ... more

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; Identify the points where the line passes.The ... more

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; Identify the points where the line passes.The ... more

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; Identify the vector parallel to the line. Since... more

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; Identify the points where the line passes.The ... more

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; Identify the points where the plane passes.The ... more

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; Write the normal vector from the the given ... more

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; Let be a point on the plane. Find its distance... more

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; Use the parametric equations, of a line passing... more

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, , , , ; Find the magnitude of using the formula... more

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, , , , ; Find the magnitude of using the formula... more

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; ; ; ; ; Find the magnitude of using the formula... more

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3; ; ; ; ; Find the magnitude of using the ... more

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; The vector with initial point and final point... more

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; The vector with initial point and terminal ... more

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4 ; A vector can be expressed using its length ... more

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; A vector can be expressed using its length ... more

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; For a vector , the horizontal and vertical ... more

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; For a vector , the horizontal and vertical ... more

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52560 ; Find the magnitude of using the formula... more

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131692 ; Find the magnitude of using the formula... more

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80 ; Find the magnitude of using the formula . ; ... more

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10100 ; Find the magnitude of using the formula... more

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Yes ; The two vectors will be perpendicular if ... more

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No, ; The two vectors will be perpendicular if ... more

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No, ; The two vectors will be perpendicular if ... more

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Yes ; The two vectors will be perpendicular if ... more

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3 ; To plot the point , move one unit along the ... more

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; To plot the point , move two units along the ... more

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; The standard equation of the sphere is:where ... more

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; The standard equation of the sphere is:where ... more

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Write the similar terms together in the given ... more

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Write the similar terms together in the given ... more

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, , , ; Find the magnitude of using the formula... more

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, , , ; Find the magnitude of using the formula... more

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; Let the given vertices of the triangle be , , ... more

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; Find the cross product of the vectors and ... more

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9 ; Substitute , , and into the formula for the ... more

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14 ; Calculate the vectors , , and .The vector in ... more

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   ; Let the point , and the vector .Substitute ... more

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   ; Let the point , and the vector .Substitute ... more

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; Find the vector with the initial point at and... more

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   ; Find the vector with the initial point at ... more

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; Let the point , and the vector .Find the ... more

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; Let the point , and the vector .Find the ... more

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; Calculate the vectors and .The vector in a ... more

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; Calculate the vectors and .The vector in a ... more

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   ; Identify the points where the line passes.The... more

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; Use the parametric equations and of a line ... more

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90 ; Substitute and into to get the ... more

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; The vector is perpendicular to both vectors ... more

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; Find vector using . Substitute the values and... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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; Find the vector at several points in the ... more

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