Answer
$1(\dfrac{1}{\sqrt 3}i +\dfrac{1}{\sqrt 3}j +\dfrac{1}{\sqrt 3}k)$
Work Step by Step
Formula to find the unit vector $\hat{\textbf{v}}$ is: $\hat{\textbf{v}}=\dfrac{v}{|v|}$
Given:$v=\dfrac{1}{\sqrt 3}i +\dfrac{1}{\sqrt 3}j +\dfrac{1}{\sqrt 3}k$; $|v|=\sqrt{(\dfrac{1}{\sqrt 3})^2+(\dfrac{1}{\sqrt 3})^2+(\dfrac{1}{\sqrt 3})^2}=1$
Thus, $\hat{\textbf{v}}=\dfrac{(\dfrac{1}{\sqrt 3}i +\dfrac{1}{\sqrt 3}j +\dfrac{1}{\sqrt 3}k)}{(1)}=(\dfrac{1}{\sqrt 3}i +\dfrac{1}{\sqrt 3}j +\dfrac{1}{\sqrt 3}k)$
and $v=|v|\hat{\textbf{v}}=1(\dfrac{1}{\sqrt 3}i +\dfrac{1}{\sqrt 3}j +\dfrac{1}{\sqrt 3}k)$
