a
(a)Given \(\overrightarrow {OA} = \overrightarrow a = 3\hat i - 6\hat j + 2\hat k\) and \(\overrightarrow {OB} = \overrightarrow b = 2\hat i + \hat j - 2\hat k\)

\(\therefore \,\,\,(\overrightarrow a \times \overrightarrow b )\, \) \(= \left| {\begin{array}{*{20}{c}}{\hat i\,\,}&{\hat j\,\,}&{\hat k}\\{\,3\,\,}&{ -6\,\,\,}&2\\{\,\,\,2\,\,\,}&{1\,\,}&{ - 2\,\,\,}\end{array}}\right|\,\) \( = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k\) \( = 10\hat i + 10\hat j + 15\hat k\) \(\Rightarrow \,\,|\overrightarrow a \times \overrightarrow b |\, = \,\sqrt {{{10}^2} + {{10}^2} + {{15}^2}} \)

\( =\sqrt {425} \) \( = 5\sqrt {17} \)

Area of \(\Delta OAB = \frac{1}{2}|\overrightarrow a \times \overrightarrow b |\, =\frac{{5\sqrt {17} }}{2}\,\)sq.unit.