Problem 4 - Unit Vectors

$v=2i-14j$
The slope of $v$ is $\frac{-14}{2}=-7$
Assume that $u=k*i+l*j$
$u$ must have a slope of $-7$ .
So: $\frac{l}{k}=-7\Rightarrow l=-7k$
Also, $u$ must be of length 1. That means:
$\sqrt{k^{2}+l^{2}}=1\Rightarrow$
$k^{2}+(-7k)^{2}=1\Rightarrow$
$50k^{2}=1\Rightarrow$
$k^{2}=\frac{1}{50}\Rightarrow$
$k=\frac{1}{5\sqrt{2}}$
And $l=\frac{-7}{5\sqrt{2}}$
Therefor:
$\boxed{u=\frac{i}{5\sqrt{2}}+\frac{-7j}{5\sqrt{2}}}$