Answer
$$\eqalign{
& \left( {\bf{a}} \right){\text{ In radians}} \cr
& \theta = 1.106{\text{rad}} \cr
& \left( {\bf{b}} \right){\text{ In degrees}} \cr
& \theta = 63.36^\circ \cr} $$
Work Step by Step
$$\eqalign{
& {\bf{u}} = 6{\bf{i}} + 2{\bf{j}} - 3{\bf{k}},{\text{ }}{\bf{v}} = {\bf{i}} + {\text{5}}{\bf{j}} \cr
& {\bf{u}} \cdot {\bf{v}} = \left( {6{\bf{i}} + 2{\bf{j}} - 3{\bf{k}}} \right) \cdot \left( {{\bf{i}} + {\text{5}}{\bf{j}}} \right) \cr
& {\bf{u}} \cdot {\bf{v}} = 6 + 10 + 0 \cr
& {\bf{u}} \cdot {\bf{v}} = 16 \cr
& \left\| {\bf{u}} \right\| = \left\| {6{\bf{i}} + 2{\bf{j}} - 3{\bf{k}}} \right\| = \sqrt {36 + 4 + 9} = 7 \cr
& \left\| {\bf{v}} \right\| = \left\| {{\bf{i}} + {\text{5}}{\bf{j}}} \right\| = \sqrt {1 + 25} = \sqrt {26} \cr
& {\text{Find the Angle Between Two Vectors}} \cr
& \cos \theta = \frac{{{\bf{u}} \cdot {\bf{v}}}}{{\left\| {\bf{u}} \right\|\left\| {\bf{v}} \right\|}} \cr
& \cos \theta = \frac{{16}}{{\left( 7 \right)\left( {\sqrt {26} } \right)}} \cr
& \theta = {\cos ^{ - 1}}\left( {\frac{{16}}{{7\sqrt {26} }}} \right) = 1.106{\text{rad}} = 63.36^\circ \cr
& \cr
& \left( {\bf{a}} \right){\text{ In radians}} \cr
& \theta = 1.106{\text{rad}} \cr
& \left( {\bf{b}} \right){\text{ In degrees}} \cr
& \theta = 63.36^\circ \cr} $$
