Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.2 Vectors - 12.2 Exercises - Page 845: 29

Answer

$\mathbf v=\langle 2,2\sqrt 3\rangle$

Work Step by Step

The component form of a vector $\mathbf v$ that make an angle $\theta$ with the positive $x$-axis is given by: $$\mathbf v=\langle |\mathbf v|\cos(\theta),|\mathbf v|\sin(\theta)\rangle$$ Substitution: $$\mathbf v=\langle 4\cos(\frac{\pi}{3}),4\sin(\frac{\pi}{3})\rangle$$ $$\mathbf v=\langle 4\cdot \frac{1}{2},4\cdot \frac{\sqrt 3}{2}\rangle$$ $$\mathbf v=\langle 2,2\sqrt 3\rangle$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.