Question

The projection of $\vec{a}=3\hat{i}-\hat{j}+5\hat{k}$ on $\vec{b}=2\hat{i}+3\hat{j}+\hat{k}$ is

• A. $\frac{8}{\sqrt{35}}$
• B. $\frac{8}{\sqrt{39}}$
• C. $\frac{8}{\sqrt{14}}$
• D. $\sqrt{14}$

Answer 1

Answer: (C)

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 $\vec{b}=\frac{\vec{a}.\vec{b}}{|\vec{b}|}$
$=\frac{\left(3\hat{i}-\hat{j}+5\hat{k}\right).\left(2\hat{i}+3\hat{j}+\hat{k}\right)}{\sqrt{2^2+3^2+1^2}}$
$=\frac{6-3+5}{\sqrt{14}}=\frac{8}{\sqrt{14}}$