A) \[\pm \,(2\hat{i}-\hat{j}-2\hat{k})~~~\]
B) \[\pm \,(3\hat{i}+\hat{j}-2\hat{k})\]
C) \[-\,(3\hat{i}+\hat{j}-3\hat{k})~\]
D) \[(3\hat{i}-\hat{j}-3\hat{k})\]
Correct Answer: A
Solution :
[a] The required vector is, \[=3\frac{(\text{\vec{A}}\times \text{\vec{B}})}{|\text{\vec{A}}\times \text{\vec{B}}|}=3\frac{[(2\hat{i}+2\hat{j}+\hat{k})\times (2\hat{i}-2\hat{j}+3\hat{k})]}{|\text{\vec{A}}\times \text{\vec{B}}|}\] \[=3\frac{(8\hat{i}-4\hat{j}-8\hat{k})}{\sqrt{{{8}^{2}}+{{4}^{2}}+{{8}^{2}}}}=2\hat{i}-\hat{j}-2\hat{k}.\]
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