Answer
$$\left\langle {\frac{2}{{\sqrt {38} }},\frac{3}{{\sqrt {38} }},\frac{5}{{\sqrt {38} }}} \right\rangle $$
Work Step by Step
$$\eqalign{
& {\bf{u}} = \left\langle {2,3,5} \right\rangle \cr
& {\text{A unit vector in the direction of }}{\bf{u}}{\text{ is }} \cr
& \frac{{\bf{u}}}{{\left\| {\bf{u}} \right\|}} = \frac{{\left\langle {2,3,5} \right\rangle }}{{\left\| {\left\langle {2,3,5} \right\rangle } \right\|}} \cr
& \frac{{\bf{u}}}{{\left\| {\bf{u}} \right\|}} = \frac{1}{{\sqrt {4 + 9 + 25} }}\left\langle {2,3,5} \right\rangle \cr
& \frac{{\bf{u}}}{{\left\| {\bf{u}} \right\|}} = \frac{1}{{\sqrt {38} }}\left\langle {2,3,5} \right\rangle \cr
& \frac{{\bf{u}}}{{\left\| {\bf{u}} \right\|}} = \left\langle {\frac{2}{{\sqrt {38} }},\frac{3}{{\sqrt {38} }},\frac{5}{{\sqrt {38} }}} \right\rangle \cr} $$
