A) \[\frac{\hat{k}+\hat{i}}{\sqrt{2}}\]
B) \[\frac{\hat{j}+\hat{k}}{\sqrt{2}}\]
C) \[\frac{\hat{i}-\hat{k}}{\sqrt{3}}\]
D) \[\frac{\hat{j}-\hat{k}}{\sqrt{2}}\]
Correct Answer: B
Solution :
Let \[\vec{a}=\hat{i}-\hat{j}+\hat{k}\] and \[\vec{b}=\hat{i}+\hat{j}-\hat{k}\] Now, \[\vec{a}\times \vec{b}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & -1 & 1 \\ 1 & 1 & -1 \\ \end{matrix} \right|\] \[=\hat{i}(1-1)-\hat{j}(-1-1)+\hat{k}(1+1)\] \[=2\hat{j}+2\hat{k}\] \[\therefore \] Required unit vector \[=\pm \frac{2\hat{j}+2\hat{k}}{\sqrt{4+4}}\] \[=\pm \frac{\hat{j}+\hat{k}}{\sqrt{2}}\]
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