Answer
Direction cosines are: $\frac{1}{3},\frac {2}{3},\frac {2}{3}$
Direction angles are: $70.5 ^\circ, 48.2^\circ, 48.2 ^\circ$
Work Step by Step
Let $v=\frac{1}{2} i+j+k=\lt \frac{1}{2} ,1,1 \gt$
$|v|=\sqrt {(\frac{1}{2} )^2+1^2+1^2}=\frac {3}{2}$
Direction cosines are: $cos \alpha = \frac{\frac {1}{2}}{\frac {3}{2}}=\frac {1}{3}, cos \beta =\frac{1}{\frac {3}{2}}=\frac {2}{3}, cos \gamma=\frac{1}{\frac {3}{2}}=\frac {2}{3}$
Thus, the direction angles are:
$ \alpha =cos^{-1} \frac {1}{3}=70.5 ^\circ, \beta = cos^{-1} \frac {2}{3}=48.2^\circ, \gamma = cos^{-1} \frac {2}{3}=48.2^ \circ$