Answer
a) $=(\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2})$
b) $=(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$
Work Step by Step
a) The magnitude of this vector is given by $\sqrt {(1)^{2} +(-1)^{2}}=\sqrt 2$.
Therefore a unit vector in direction $u$ is given by:
$\frac{1}{\sqrt 2}(1,-1)$
$=(\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2})$
b) a unit vector in the opposite direction is given by multiplying the unit vector found in part a) by $(-1)$
This is equal to $(-1)\times(\frac{1}{\sqrt 2},-\frac{1}{\sqrt 2})$
$=(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$
