Find the unit vector in the direction of the vector
$\vec a = \hat i + \hat j + 2\hat k$.

We have, $\vec a = \hat i + \hat j + 2\hat k$
$\Rightarrow |a| = \sqrt {{1^2} + {1^2} + {1^2}} = \sqrt {1 + 1 + 4} = \sqrt 6$
$\therefore$

Unit vector in the direction of vector
$= \cfrac{{\vec a}}{{|\vec a|}} = \cfrac{{\hat i + \hat j + 2\hat k}}{{\sqrt 6 }} = \cfrac{1}{{\sqrt 6 }}\hat i + \cfrac{1}{{\sqrt 6 }}\hat j + \cfrac{2}{{\sqrt 6 }}\hat k$