A) \[\frac{2\mathbf{i}-\mathbf{j}+\mathbf{k}}{\sqrt{6}}\]
B) \[\frac{2\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{6}}\]
C) \[\frac{-2\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{6}}\]
D) \[\frac{2\mathbf{i}+\mathbf{j}-\mathbf{k}}{\sqrt{6}}\]
Correct Answer: B
Solution :
A vector perpendicular to the plane determined by the points \[P(1,\,-1,\,2);\] \[Q(2,\,0,\,-1)\] and \[R(0,\,2,\,1)\] is given by \[\overrightarrow{QR}\times \overrightarrow{PR}\Rightarrow (-2\mathbf{i}+2\mathbf{j}+2\mathbf{k})\times (-\mathbf{i}+3\mathbf{j}-\mathbf{k})\] Therefore, unit vector \[=\frac{2\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{4+1+1}}=\frac{2\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{6}}.\]You need to login to perform this action.
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