A) \[9\]
B) \[21\]
C) \[13\]
D) \[7\]
Correct Answer: C
Solution :
\[\vec{a}=\hat{i}+2\hat{j}+3\hat{k}\] \[\hat{b}=-\hat{i}+2\hat{j}+3\hat{k}\] \[\vec{c}=2\hat{i}-2\hat{j}-3\hat{k}\] \[\Rightarrow \] \[(\vec{b}\,+\,\vec{c})=\hat{i}\] and \[(\vec{b}\,+\vec{c})\times \vec{a}\,=\hat{i}\,\times (\hat{i}+2\hat{j}+3\hat{k})\] \[=2\hat{k}-3\hat{j}\] \[\left( \begin{align} & \because \,\,\,\hat{i}\times \hat{j}=\hat{k}, \\ & \hat{i}\times \hat{k}=-\hat{j} \\ \end{align} \right)\] Now, \[\vec{a}\,\times \,\{(\vec{b}\,\,+\,\vec{c})\times \vec{a}\}\] \[=\hat{i}.\,(13\,\hat{i}-2\hat{j}-3\hat{k})\] \[=13\]
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