A) \[\frac{5\mathbf{i}-3\mathbf{j}+9\mathbf{k}}{\sqrt{115}}\]
B) \[\frac{5\mathbf{i}+3\mathbf{j}-9\mathbf{k}}{\sqrt{115}}\]
C) \[\frac{-5\mathbf{i}+3\mathbf{j}-9\mathbf{k}}{\sqrt{115}}\]
D) \[\frac{5\mathbf{i}+3\mathbf{j}+9\mathbf{k}}{\sqrt{115}}\]
Correct Answer: C
Solution :
\[\mathbf{a}\times \mathbf{b}=\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 3 & 2 & -1 \\ 12 & 5 & -5 \\ \end{matrix} \right|=-5\,\mathbf{i}+3\mathbf{j}-9\mathbf{k}.\] Unit vector along \[\mathbf{a}\times \mathbf{b}=\frac{-5\mathbf{i}+3\mathbf{j}-9\mathbf{k}}{\sqrt{115}}.\]
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