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.
Starting from the point (0,a,0)
(please see attached image)
we draw the vector $a\hat{i}$, reaching (a,a,0)
We then add $-a\hat{j} $(it points in the -y direction)and reach (a,0,0)
We then add $a\hat{k}$ and reach the opposite corner.
Thus ,
$\vec{v}= a\hat{i} - a\hat{j }+a\hat{k}$
