Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.6 Vectors in Space - 8.6 Assess Your Understanding - Page 646: 65


$\alpha\approx60.9^\circ,\beta\approx144.2^\circ,\gamma\approx71.1^\circ$, $\vec v=\sqrt {38}(cos60.9^\circ i+cos144.2^\circ j+cos71.1^\circ k)$

Work Step by Step

1. Given $\vec v=3i-5j+2k$, we have $||\vec v||=\sqrt {9+25+4}=\sqrt {38}$ 2. We have $\alpha=cos^{-1}(\frac{3}{\sqrt {38}})\approx60.9^\circ$ 3. We have $\beta=cos^{-1}(\frac{-5}{\sqrt {38}})\approx144.2^\circ$ 4. We have $\gamma=cos^{-1}(\frac{2}{\sqrt {38}})\approx71.1^\circ$ 5. We have $\vec v=\sqrt {38}(cos60.9^\circ i+cos144.2^\circ j+cos71.1^\circ k)$
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.