Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 235: 13

$v=(2\sqrt 2, 2\sqrt 2)$

a) The magnitude of this vector is given by $\sqrt {(1)^{2} +(1)^{2}}=\sqrt {2}$. Therfore 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, $4$ has length $4$, so is given by $4\times(\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2})$ $=(2\sqrt 2, 2\sqrt 2)$