Answer
$$\eqalign{
& \left( {\bf{a}} \right)0.19{\text{radians}} \cr
& \left( {\bf{b}} \right)10.89^\circ \cr} $$
Work Step by Step
$$\eqalign{
& {\bf{u}} = 2{\bf{i}} - 3{\bf{j}} + {\bf{k}},{\text{ }}{\bf{v}} = {\bf{i}} - 2{\bf{j}} + {\bf{k}} \cr
& {\bf{u}} \cdot {\bf{v}} = \left( {2{\bf{i}} - 3{\bf{j}} + {\bf{k}}} \right) \cdot \left( {{\bf{i}} - 2{\bf{j}} + {\bf{k}}} \right) \cr
& {\bf{u}} \cdot {\bf{v}} = 2 + 6 + 1 = 9 \cr
& \left\| {\bf{u}} \right\| = \left\| {2{\bf{i}} - 3{\bf{j}} + {\bf{k}}} \right\| = \sqrt {4 + 9 + 1} = \sqrt {14} \cr
& \left\| {\bf{v}} \right\| = \left\| {{\bf{i}} - 2{\bf{j}} + {\bf{k}}} \right\| = \sqrt {1 + 4 + 1} = \sqrt 6 \cr
& \cos \theta = \frac{{{\bf{u}} \cdot {\bf{v}}}}{{\left\| {\bf{u}} \right\|\left\| {\bf{v}} \right\|}} \cr
& \cos \theta = \frac{9}{{\sqrt {14} \sqrt 6 }} \cr
& \theta = {\cos ^{ - 1}}\left( {\frac{9}{{\sqrt {14} \sqrt 6 }}} \right) \cr
& \left( {\bf{a}} \right){\text{ In radians}} \cr
& \theta = 0.19{\text{radians}} \cr
& \left( {\bf{b}} \right){\text{ In degrees}} \cr
& \theta = 10.89^\circ \cr} $$
