A) \[\hat{i}+2\hat{j}-4\hat{k}\]
B) \[-\hat{i}-3\hat{j}+4\hat{k}\]
C) \[-\hat{i}-5\hat{j}+4\hat{k}\]
D) \[-2\hat{i}-\hat{j}+\hat{k}\]
Correct Answer: B
Solution :
\[\overrightarrow{A}=2\hat{i}-2\hat{j}-\hat{k},\overrightarrow{B}=-\hat{i}+3\hat{j}+2\hat{k}\] \[\therefore \] \[\overrightarrow{A}\times \overrightarrow{B}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 2 & -2 & -1 \\ -1 & 3 & 2 \\ \end{matrix} \right|\] \[=\hat{i}(-4+3)-\hat{j}(4-1)+\hat{k}(6-2)\] \[=-\hat{i}-3\hat{j}+4\hat{k}\]
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