Answer
$v=(2\sqrt 2, -2\sqrt 2)$
Work Step by Step
The magnitude of vector, $u$ is given by $\sqrt {(1)^{2}+(-1)^{2}}=\sqrt 2$
Hence a unit vector in the same direction as $u$ is given by $\frac{1}{\sqrt 2}\times(1,-1)$
$=(\frac{1}{\sqrt 2}, -\frac{1}{\sqrt 2})$
Vector, $v$ has length 4, so must be equal to $4\times(\frac{1}{\sqrt 2}, -\frac{1}{\sqrt 2})$
$=(\frac{4}{\sqrt 2}, -\frac{4}{\sqrt 2})$
Therefore, $v=(2\sqrt 2, -2\sqrt 2)$