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