A) \[\frac{1}{\sqrt{14}}\]
B) \[\frac{2}{\sqrt{14}}\]
C) \[\frac{2}{\sqrt{17}}\]
D) None of these
Correct Answer: B
Solution :
Let \[\overrightarrow{a}=2\hat{i}+3\hat{j}-2\hat{k}\] and \[\overrightarrow{b}=\hat{i}+2\hat{j}+3\hat{k}\] Projection of\[\overrightarrow{a}\]on \[\overrightarrow{b}=\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}\] \[=\frac{(2\hat{i}+3\hat{j}-2\hat{k}).(\hat{i}+2\hat{j}+3\hat{k})}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}}\] \[=\frac{2+6-6}{\sqrt{1+4+9}}\] \[=\frac{2}{\sqrt{14}}\]
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