Answer
$\vec{v}= a\hat{i} + a\hat{j }+a\hat{k}$
Work Step by Step
Two vectors $\vec{a}$ and $\vec{b}$ may be added geometrically by drawing them to a common scale and placing them head to tail.
Please see attached image.
The vector $\vec{v},$ beginning at (0,0,0) and ending in (a,a,a) is obtained by
starting from (0,0,0) , with vector $a\hat{i}$
reaching point (a,0,0), adding vector $a\hat{j },$
reaching point(a,a,0) and adding vector $a\hat{k}$.
Thus $\vec{v}= a\hat{i} + a\hat{j }+a\hat{k}$
