Explanation

(a)
We know, if $\theta$ is the angle between $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$, then
$\cos{\theta = \frac{\overrightarrow{\mathbf{a}}\mathbf{\bullet}\overrightarrow{\mathbf{b}}}{\left| \overrightarrow{\mathbf{a}} \right|\mathbf{|}\overrightarrow{\mathbf{b}}\mathbf{|}\ }}$
$= \frac{\left( 2\widehat{\mathbf{i}} + 2\widehat{\mathbf{j}} - \widehat{\mathbf{k}} \right) \bullet (6\widehat{\mathbf{i}} - 3\widehat{\mathbf{j}} + 2\widehat{\mathbf{k}})}{\sqrt{2^{2} + 2^{2} + ( - 1)^{2}}\sqrt{6^{3} + ( - 3)^{2} + 2^{2}}}$
$= \frac{12 - 6 - 2}{\sqrt{4 + 4 + 1}\sqrt{36 + 9 + 4}}$
$= \frac{4}{\sqrt{9}\sqrt{49}} = \frac{4}{21}$