Answer
$-7 \ i+ 7 \sqrt 3 \ j$
Work Step by Step
Let us consider that a vector $v$ is given by $v=pi+qj$ and makes an angle of $\alpha$ with the positive $x$-axis. The magnitude of the vector can be determined using the formula:
$||v||=\sqrt{p^2+q^2} $
Then we find $p=||v||cos\alpha$ and $v=||v||sin\alpha$.
Here, we have: $p=||14|| \cos \ (120^\circ)= -7$
and $v=||14|| \sin \ (120^\circ)=7 \sqrt 3$
Therefore $v=-7 \ i+ 7 \sqrt 3 \ j$
