Question

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

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

Answer 1

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

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