A) \[\frac{1}{\sqrt{14}}\]
B) \[\frac{2}{\sqrt{14}}\]
C) \[\sqrt{14}\]
D) \[\frac{-2}{\sqrt{14}}\]
Correct Answer: B
Solution :
Here, \[\overrightarrow{a}=2\,\hat{i}\,+3\,\hat{j}-2\,\hat{k}\] and \[\overrightarrow{b}=\hat{i}+2\hat{j}+3\,\hat{k}\] \[\therefore \] Projection of \[\overrightarrow{a}=2\hat{i}+3\hat{j}-3\,\hat{k}\] on \[\overrightarrow{b}=\hat{i}+2\hat{j}+3\hat{k}\] is \[=\frac{\overrightarrow{a}\,.\,\,\overrightarrow{b}}{|\overrightarrow{b}|}\] \[=\frac{2\times 1+3\times 2-2\times 3}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}}\] \[=\frac{2}{\sqrt{14}}\]
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