A) \[\frac{(-3\mathbf{i}+5\mathbf{j}+11\mathbf{k})}{\sqrt{155}}\]
B) \[\frac{(3\mathbf{i}-5\mathbf{j}+11\mathbf{k})}{\sqrt{155}}\]
C) \[\frac{(6\mathbf{i}-4\mathbf{j}-\mathbf{k})}{\sqrt{53}}\]
D) \[\frac{(5\mathbf{i}+3\mathbf{j})}{\sqrt{34}}\]
Correct Answer: A
Solution :
Let \[\mathbf{a}=2\mathbf{i}-\mathbf{j}+\mathbf{k}\] and \[\mathbf{b}=3\mathbf{i}+4\mathbf{j}-\mathbf{k},\] then a unit vector perpendicular to \[\mathbf{a}\] and \[\mathbf{b}\] is \[\frac{\mathbf{a}\times \mathbf{b}}{|\mathbf{a}\times \mathbf{b}|}\] Here \[\mathbf{a}\times \mathbf{b}=-3\mathbf{i}+5\mathbf{j}+11\mathbf{k}\] Unit vector is \[\frac{-3\mathbf{i}+5\mathbf{j}+11\mathbf{k}}{\sqrt{155}}\].
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