Answer
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$
