Answer
a) $=(-\frac{5}{13}, \frac{12}{13})$
b) $=(\frac{5}{13}, -\frac{12}{13})$
Work Step by Step
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
$-1\times (-\frac{5}{13}, \frac{12}{13})$
$=(\frac{5}{13}, -\frac{12}{13})$