A) \[\sqrt{15}\]
B) \[3\sqrt{5}\]
C) \[\frac{3}{2}\sqrt{10}\]
D) \[\frac{5\sqrt{5}}{3}\]
Correct Answer: C
Solution :
\[\Delta =\frac{1}{2}|\mathbf{a}\times \mathbf{b}|=\frac{1}{2}\left| \,\left| \,\begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 3 & 2 & -1 \\ 1 & 3 & 1 \\ \end{matrix}\, \right|\, \right|\,\,=\frac{1}{2}|(5\mathbf{i}-4\mathbf{j}+7\mathbf{k})|\] \[\Delta =\frac{1}{2}\sqrt{25+16+49}=\frac{1}{2}\sqrt{90}=\frac{3}{2}\sqrt{10}.\]
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