A) \[\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}-\hat{k})\]
B) \[\frac{1}{\sqrt{3}}(-\hat{i}+\hat{j}+\hat{k})\]
C) \[\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}+\hat{k})\]
D) \[\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\]
Correct Answer: B
Solution :
As \[\hat{n}=\frac{A\times B}{|A\times B|}\] \[A\times B\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 1 & 0 \\ 0 & 1 & -1 \\ \end{matrix} \right|=\hat{i}\,(-1-0)-\hat{j}(-1-0)+\hat{k}(1-0)\] \[=-\hat{i}+\hat{j}+\hat{k}\] \[\therefore \] \[|A\times B|=\sqrt{3},\] \[\hat{n}=\frac{1}{\sqrt{3}}(-\hat{i}+\hat{j}+\hat{k})\]
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