A) \[\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]
B) \[\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\]
C) \[\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\]
D) None of these
Correct Answer: A
Solution :
Let\[\overrightarrow{a}=3\hat{i}+\hat{j}+2\hat{k}\]and\[\overrightarrow{b}=2\hat{i}-2\hat{j}+4\hat{k}\] Now, \[\overrightarrow{a}\times \overrightarrow{b}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 3 & 1 & 2 \\ 2 & -2 & 4 \\ \end{matrix} \right|\] \[=\hat{i}(4+4)-\hat{j}(12-4)+\hat{k}(-6-2)\] \[=8\hat{i}-8\hat{j}-8\hat{k}\] \[\therefore \]Required unit vector \[=\frac{\overrightarrow{a}\times \overrightarrow{b}}{|\overrightarrow{a}\times \overrightarrow{b}|}\] \[=\frac{8(\hat{i}-\hat{j}-\hat{k})}{8\sqrt{{{1}^{2}}+{{1}^{2}}+{{1}^{2}}}}\] \[=\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
