A) \[4(2\hat{i}+2\hat{j}-\hat{k})\]
B) \[4(-2\hat{i}-2\hat{j}+\hat{k})\]
C) \[4(2\hat{i}-2\hat{j}-\hat{k})\]
D) \[4(2\hat{i}+2\hat{j}+\hat{k})\]
Correct Answer: C
Solution :
\[(\vec{a}+\vec{b})\times (\vec{a}-\vec{b})\] \[=2\,(\vec{b}\times \vec{a})\] \[=2\,\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 2 & -2 \\ 3 & 2 & 2 \\ \end{matrix} \right|\]\[=2(8\hat{i}-8\hat{j}+4\hat{k})\] Required vector\[=\pm 12\frac{(2\hat{i}-2\hat{j}-\hat{k})}{3}\] \[=\pm 4(2\hat{i}-2\hat{j}-\hat{k})\]You need to login to perform this action.
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