Explanation

(c)
Let the position vectors of the points $A,B,C$ are $\overrightarrow{\mathbf{0}},\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}},\ \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}$ respectively and θ$= 90{^\circ}$
$\therefore Area\ of\ triangle = \frac{1}{2}|\overrightarrow{\mathbf{AB}} \times \overrightarrow{\mathbf{AC}}|$
$= \frac{1}{2}|\left( \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right) \times \left( \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}} \right)|$
$= \frac{1}{2}\left| 2\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}} \right|$
$= |\overrightarrow{\mathbf{b}}|\ |\overrightarrow{\mathbf{a}}|$ $\sin\theta = 3 \times 2\sin{90{^\circ}} = 6$