A) \[\frac{-2i+3\vec{j}+5\vec{k}}{\sqrt{30}}\]
B) \[\frac{-2i+5\vec{j}+6\vec{k}}{\sqrt{38}}\]
C) \[\frac{-2\vec{i}+3\vec{j}+5\vec{k}}{\sqrt{38}}\]
D) none of these
Correct Answer: C
Solution :
\[\vec{a}=\vec{i}-\vec{j}+\vec{k}\]and \[\vec{b}=2\vec{i}+3\vec{j}-\vec{k}\] \[\vec{a}\times \vec{b}=\vec{i}[1-3]-\vec{j}[1-1-2]\] \[+\,\vec{k}+\vec{k}[3+2]=-2\vec{i}+3\vec{j}+5\vec{k}\] \[|\vec{a}\times \vec{b}|=\sqrt{{{(-2)}^{2}}+{{(3)}^{2}}+{{(5)}^{2}}}=\sqrt{38}\] Therefore unit vector \[\frac{\vec{a}\times \vec{b}}{|\vec{a}\times \vec{b}|}=\frac{2\vec{i}+3\vec{j}+5\vec{k}}{\sqrt{38}}\]
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