A) \[\frac{-2i+3j+5k}{\sqrt{30}}\]
B) \[\frac{-2\mathbf{i}+5\mathbf{j}+6\mathbf{k}}{\sqrt{38}}\]\[\]
C) \[\frac{-2i+3j+5k}{\sqrt{38}}\]
D) \[\frac{-2i+4j+5k}{\sqrt{38}}\]
Correct Answer: C
Solution :
Vectors \[\mathbf{a}=\mathbf{i}-\mathbf{j}+\mathbf{k}\] and \[\mathbf{b}=2\mathbf{i}+3\mathbf{j}-\mathbf{k}\]. We know that\[\mathbf{a}\times \mathbf{b}=\mathbf{i}(1-3)-\mathbf{j}(-1-2)+\mathbf{k}(3+2)\] \[=-\,2\mathbf{i}+3\mathbf{j}+5\mathbf{k}\] and \[|\mathbf{a}\times \mathbf{b}|\,\]\[=\sqrt{{{(-2)}^{2}}+{{(3)}^{2}}+{{(5)}^{2}}}=\sqrt{38}\] Therefore unit vector \[\frac{\mathbf{a}\times \mathbf{b}}{|\mathbf{a}\times \mathbf{b}|}=\frac{-2\mathbf{i}+3\mathbf{j}+5\mathbf{k}}{\sqrt{38}}\].
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