Find the unit vector in the direction of vector $\overrightarrow {PQ}$, where $P$ and $Q$ are the points $(1,2,3)$ and $(4,5,6)$ respectively.

$\overrightarrow {PQ} =$position vector of $Q -$position vector of $P$

$= (4\hat i + 5\hat j + 6\hat k) - (\hat i + 2j + 3\hat k) = 3\hat i + 3\hat j + 3\hat k$
$\therefore$ $|\overrightarrow {PQ} | = \sqrt {{3^2} + {3^2} + {3^2}} = \sqrt {9 + 9 + 9} = \sqrt {27} = 3\sqrt 3$

$\therefore$

Unit vector in the direction of $\overrightarrow {PQ}$

$\cfrac{{\overrightarrow {PQ} }}{{|\overrightarrow {PQ} |}} = \cfrac{{3\hat i + 3\hat j + 3\hat k}}{{3\sqrt 3 }} = \cfrac{1}{{\sqrt 3 }}\hat i + \cfrac{1}{{\sqrt 3 }}\hat j + \cfrac{1}{{\sqrt 3 }}\hat k$