A) \[20\mathbf{i}-3\mathbf{j}+7\mathbf{k}\]
B) \[20\mathbf{i}-3\mathbf{j}-7\mathbf{k}\]
C) \[20\mathbf{i}+3\mathbf{j}-7\mathbf{k}\]
D) None of these
Correct Answer: A
Solution :
\[\mathbf{a}\times (\mathbf{b}\times \mathbf{c})=\mathbf{a}\times \left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & -1 & 1 \\ 1 & 3 & -1 \\ \end{matrix} \right|=\mathbf{a}\times (-2\mathbf{i}+3\mathbf{j}+7\mathbf{k})\] \[=\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & -2 \\ -2 & 3 & 7 \\ \end{matrix} \right|=20\mathbf{i}-3\mathbf{j}+7\mathbf{k}.\]
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