A) \[\frac{\sqrt{115}}{\sqrt{14}\sqrt{194}}\]
B) \[\frac{51}{\sqrt{14}\sqrt{144}}\]
C) \[\frac{\sqrt{64}}{\sqrt{14}\sqrt{194}}\]
D) None of these
Correct Answer: A
Solution :
\[\mathbf{a}\times \mathbf{b}=\left| \,\begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 3 & 2 & -1 \\ 12 & 5 & -5 \\ \end{matrix}\, \right|=-5\mathbf{i}+3\mathbf{j}-9\mathbf{k}\] \[\Rightarrow \sin \theta =\frac{\sqrt{25+9+81}}{\sqrt{14}.\sqrt{194}}=\frac{\sqrt{115}}{\sqrt{14}.\sqrt{194}}\].
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