A) \[\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]
B) \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\]
C) \[\frac{-\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]
D) \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\]
Correct Answer: A
Solution :
[a] Angle between \[\vec{A}\] and \[\vec{B}\] is given by \[\cos \theta =\frac{\text{\vec{A}}\,\text{.}\,\text{\vec{B}}}{\text{AB}}=\frac{3}{\sqrt{21}}\] The unit vector perpendicular to \[\vec{A}\] and \[\vec{B}\] is given by \[\hat{n}=\frac{\text{\vec{A}}\times \text{\vec{B}}}{|\text{\vec{A}}\times \text{\vec{B}}|}=\frac{(3\hat{i}+\hat{j}+2\hat{k})\times (2\hat{i}-2\hat{j}+4\hat{k})}{|(3\hat{i}+\hat{j}+2\hat{k})\times (2\hat{i}-2\hat{j}+4\hat{k})|}\] \[=\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]You need to login to perform this action.
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