## Elementary Linear Algebra 7th Edition

a) $=(-\frac{5}{13}, \frac{12}{13})$ b) $=(\frac{5}{13}, -\frac{12}{13})$
a) The magnitude of the vector $=\sqrt {(-5)^{2}+(12)^{2}}$ $=\sqrt {169}$ $=13$ Therefore a unit vector in the same direction as $u$ is equal to: $\frac{1}{13}(-5,12)$ $=(-\frac{5}{13}, \frac{12}{13})$. b) The unit vector will go in the opposite direction, if it is multiplied by $-1$. Hence a unit vector going in the opposite direction of $u$ is given by $-1\times (-\frac{5}{13}, \frac{12}{13})$ $=(\frac{5}{13}, -\frac{12}{13})$