A) \[-\frac{3}{\sqrt{14}}\]
B) \[\frac{3}{\sqrt{14}}\]
C) \[-\frac{\sqrt{3}}{2}\]
D) \[\frac{3}{\sqrt{2}}\]
Correct Answer: C
Solution :
Let at \[\vec{a}=2\,\,\hat{i}+\hat{j}-3\hat{k}\] and \[\vec{b}=\hat{i}-2\hat{j}+\hat{k}\] projection of \[\vec{a}\] on \[\vec{b}=\frac{\vec{a}\,.\,\,\vec{b}}{|\vec{b}|}\] \[=\frac{(2\,\hat{i}+\hat{j}=3\hat{k})\,.\,\,(\hat{i}-2\hat{j}+\hat{k})}{\sqrt{{{1}^{2}}+{{(-2)}^{2}}+{{1}^{2}}}}\] \[=\frac{2-2-3}{\sqrt{6}}=-\frac{3}{\sqrt{6}}=-\frac{\sqrt{3}}{2}\]
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