Answer
a) $=(-\frac{1}{\sqrt {26}},\frac{3}{\sqrt {26}}, \frac{4}{\sqrt {26}})$
b) $=(\frac{1}{\sqrt {26}},-\frac{3}{\sqrt {26}}, -\frac{4}{\sqrt {26}})$
Work Step by Step
a) The magnitude of this vector is given by $\sqrt {(-1)^{2} +(3)^{2}+(4)^{2}}=\sqrt {26}$.
Therefore a unit vector in direction $u$ is given by:
$\frac{1}{\sqrt {26}}(1,3,4)$
$=(-\frac{1}{\sqrt {26}},\frac{3}{\sqrt {26}}, \frac{4}{\sqrt {26}})$
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 $(-1)\times(-\frac{1}{\sqrt {26}},\frac{3}{\sqrt {26}}, \frac{4}{\sqrt {26}})$
$=(\frac{1}{\sqrt {26}},-\frac{3}{\sqrt {26}}, -\frac{4}{\sqrt {26}})$
