A) \[\frac{\mathbf{i}-\mathbf{j}}{\sqrt{2}}\]
B) \[\frac{\mathbf{i}+\mathbf{k}}{\sqrt{2}}\]
C) \[\frac{\mathbf{j}-\mathbf{k}}{\sqrt{2}}\]
D) \[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}\]
Correct Answer: D
Solution :
Unit vectors perpendicular to the plane of \[\mathbf{a}\] and \[\mathbf{b}\] = \[\pm \frac{\mathbf{a}\times \mathbf{b}}{|\mathbf{a}\times \mathbf{b}|}\] \[\therefore \] Required vector is \[\pm \frac{(\mathbf{i}-\mathbf{j}+\mathbf{k})\times (-\mathbf{i}+\mathbf{j}+\mathbf{k})}{\left| (\mathbf{i}-\mathbf{j}+\mathbf{k})\times (-\mathbf{i}+\mathbf{j}+\mathbf{k}) \right|}\] \[=\pm \frac{(-(\mathbf{i}+\mathbf{j}))}{\sqrt{2}}i.e.,\ \frac{-(\mathbf{i}+\mathbf{j})}{\sqrt{2}}\] and \[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}\].
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