# Chapter 12 - Section 12.3 - The Dot Product - 12.3 Exercises - Page 813: 34

Direction cosines are: $\frac{6}{7}, \frac{3}{7}, \frac{-2}{7}$ Direction angles are: $31 ^\circ, 65 ^\circ, 107 ^\circ$

#### Work Step by Step

Let $v= \lt 6,3,-2 \gt$ $|v|=\sqrt {6^2+3^2+(-2)^2}=7$ Direction cosines are: $cos \alpha = \frac{6}{7}, cos \beta =\frac{3}{7}, cos \gamma=\frac{-2}{7}$ Thus, the direction angles are: $\alpha =cos^{-1} \frac{6}{7}=31 ^\circ, \beta = cos^{-1} \frac{3}{7}=65 ^\circ, \gamma = cos^{-1} \frac{-2}{7}=107^ \circ$

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.