Explanation

(a)
$\cos{\theta = \frac{\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}}{\left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|}}$
$= \frac{\left( 2\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}} \right) \bullet (6\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}})}{\sqrt{2^{2} + 2^{2} + ({- 1)}^{2}}\sqrt{6^{2} + {( - 3)}^{2} + 2^{2}}}$
$= \frac{12 - 6 - 2}{\sqrt{4 + 4 + 1}\sqrt{36 + 9 + 4}} = \frac{4}{21}$