Explanation Given data: Write the given polar coordinate points as follows: a. ( − 2 , π 3 ) b. ( 2 , − π 3 ) c. ( r , θ ) d. ( r , θ + π ) e. ( r , θ ) f. ( 2 , − 2 π 3 ) g. ( − r , θ + π ) h. ( − 2 , 2 π 3 ) Formula used: Write the expression for polar coordinate pair for the polar coordinate point ( r , θ ) as follows: ( r , θ ) = ( r , θ ± 2 n π ) ( r , θ ) = ( − r , θ ± ( 2 n + 1 ) π ) Here, n = 0 , 1 , 2 , 3 , .... Calculation: Polar coordinate pair for a. ( − 2 , π 3 ) : From the polar coordinate pair equations, substitute − 2 for r , π 3 for θ , 0 for n and obtain the polar coordinate pair for the polar coordinate point ( − 2 , π 3 ) as follows: ( − 2 , π 3 ) = ( − 2 , π 3 ± 2 ( 0 ) π ) = ( − 2 , π 3 ) ( − 2 , π 3 ) = ( − ( − 2 ) , π 3 ± ( 2 ( 0 ) + 1 ) π ) = ( 2 , π 3 ± π ) = ( 2 , 4 π 3 ) , or ( 2 , − 2 π 3 ) Therefore, the polar coordinate pair for ( − 2 , π 3 ) are ( 2 , 4 π 3 ) or ( 2 , − 2 π 3 ) . From the given points, f. ( 2 , − 2 π 3 ) is the correct polar coordinate pair for ( − 2 , π 3 ) . Polar coordinate pair for b. ( 2 , − π 3 ) : From the polar coordinate pair equations, substitute 2 for r , − π 3 for θ , 0 for n and obtain the polar coordinate pair for the polar coordinate point ( 2 , − π 3 ) as follows: ( 2 , − π 3 ) = ( 2 , − π 3 ± 2 ( 0 ) π ) = ( 2 , − π 3 ) ( 2 , − π 3 ) = ( − 2 , − π 3 ± ( 2 ( 0 ) + 1 ) π ) = ( − 2 , − π 3 ± π ) = ( − 2 , 2 π 3 ) or ( − 2 , − 4 π 3 ) Therefore, the polar coordinate pair for ( 2 , − π 3 ) are ( − 2 , 2 π 3 ) or ( − 2 , − 4 π 3 )

Thomas' Calculus: Early Transcendentals in SI Units

14th Edition

ISBN: 9781292253114

Author: Hass, Joel R., Heil, Christopher E., WEIR, Maurice D.

Publisher: PEARSON

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Chapter 11.3, Problem 2E

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Identify the polar coordinate pairs those label the same point.

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Chapter 11.3, Problem 1E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 11 Solutions

Thomas' Calculus: Early Transcendentals in SI Units

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...

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