Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 235: 15

$v=(1,\sqrt {3} ,0)$

The magnitude of vector, $u$ is given by $\sqrt {(\sqrt 3)^{2}+(3)^{2}+(0)^{2}}=\sqrt {12}$ Hence a unit vector in the same direction as $u$ is given by $\frac{1}{\sqrt {12}}\times(\sqrt 3), 3,0)$ $=(\frac{1}{2}, \frac{\sqrt 3}{2}, 0)$ Vector, $v$ has length 2, so must be equal to $2\times(\frac{1}{2}, \frac{\sqrt 3}{2}, 0)$ $=(1,\sqrt {3} ,0)$ Therefore $v=(2\sqrt 2, -2\sqrt 2)$