Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that consists of two line segments C1 and C2, where C1 has vertices (−1, 0) and (0, 1) and C2 has vertices (0, 1) and (1, 0). C is oriented clockwise. (a) Sketch C accurately. (b) Find the work done by F by moving a particle along the path C in the given direction.

Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that consists of two line segments C1 and C2, where C1 has vertices (−1, 0) and (0, 1) and C2 has vertices (0, 1) and (1, 0). C is oriented clockwise. (a) Sketch C accurately. (b) Find the work done by F by moving a particle along the path C in the given direction.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 22E

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Question

Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that
consists of two line segments C1 and C2, where C1 has vertices (−1, 0) and (0, 1)
and C2 has vertices (0, 1) and (1, 0). C is oriented clockwise.
(a) Sketch C accurately.
(b) Find the work done by F by moving a particle along the path C in the given
direction.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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