Answer
$$\eqalign{
& \left( {\bf{a}} \right)\left\langle {\frac{3}{5},0,\frac{4}{5}} \right\rangle \cr
& \left( {\bf{b}} \right) - \left\langle {\frac{3}{5},0,\frac{4}{5}} \right\rangle \cr} $$
Work Step by Step
$$\eqalign{
& {\bf{v}} = \left\langle {6,0,8} \right\rangle \cr
& {\text{Find }}\left\| {\bf{v}} \right\| \cr
& \left\| {\bf{v}} \right\| = \sqrt {{{\left( 6 \right)}^2} + {{\left( 0 \right)}^2} + {{\left( 8 \right)}^2}} \cr
& \left\| {\bf{v}} \right\| = \sqrt {100} \cr
& \left\| {\bf{v}} \right\| = 10 \cr
& \left( {\bf{a}} \right){\text{ A unit vector in the direction of }}{\bf{v}}{\text{ is}} \cr
& \frac{1}{{\left\| {\bf{v}} \right\|}}{\bf{v}} = \frac{1}{{10}}\left\langle {6,0,8} \right\rangle \cr
& \frac{1}{{\left\| {\bf{v}} \right\|}}{\bf{v}} = \left\langle {\frac{3}{5},0,\frac{4}{5}} \right\rangle \cr
& \left( {\bf{b}} \right){\text{ A unit vector in the opposite direction of }}{\bf{v}}{\text{ is}} \cr
& - \frac{1}{{\left\| {\bf{v}} \right\|}}{\bf{v}} = - \left\langle {\frac{3}{5},0,\frac{4}{5}} \right\rangle \cr} $$
