A) \[\frac{8}{\sqrt{35}}\]
B) \[\frac{8}{\sqrt{39}}\]
C) \[\frac{8}{\sqrt{14}}\]
D) \[\sqrt{14}\]
Correct Answer: C
Solution :
Given, \[\vec{a}=3\hat{i}-\hat{j}+5\hat{k}\] and \[\vec{b}=2\hat{i}+3\hat{j}+\hat{k}\] The projection of \[\vec{a}\] on \[\vec{b}=\frac{\vec{a}.\vec{b}}{|\vec{b}|}\] \[=\frac{(3\hat{i}-\hat{j}+5\hat{k}).(2\hat{i}+3\hat{j}+\hat{k})}{\sqrt{{{2}^{2}}+{{3}^{2}}+{{1}^{2}}}}\] \[=\frac{6-3+5}{\sqrt{14}}=\frac{8}{\sqrt{14}}\]
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