Question

There are two vectors $\overrightarrow{A}=3\hat{i}+\hat{j}$ and $\overrightarrow{B}=\hat{j}+2\hat{k}.$ Find the magnitude of component of $\overrightarrow{A}$ along $\overrightarrow{B}$

• A. $\frac{1}{5\sqrt{2}}$
• B. $\frac{3}{5\sqrt{2}}$
• C. $\frac{1}{\sqrt{5}}$
• D. $\frac{1}{\sqrt{10}}$

Answer 1

The correct option is C $\frac{1}{\sqrt{5}}$

Magnitude of component of $\overrightarrow{A}$ along $\overrightarrow{B}=\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{B}|}$
$=\frac{3\times 0+1\times 1+2\times 0}{\sqrt{1^2+2^2}}$
$=\frac{1}{\sqrt{5}}$