Question

$\hat{i}$ and $\hat{j}$ are unit vector along x and y-axis respectively What is the component of a vector

A = 2 $\hat{i}$ + 3$\hat{j}$ along the direction $\hat{i}$ + $\hat{j}$?

• A. 5
• B.
• C.
• D. None of these

Answer 1

The correct option is B

Let
$\overrightarrow{A}=\widehat{2i}+\widehat{3j}\overrightarrow{B}=\hat{i}+\hat{j}Componentof\overrightarrow{A}along\overrightarrow{B},Acos\theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{B}\Rightarrow Acos\theta =\frac{(\widehat{2i}+\widehat{3j}).(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{5}{\sqrt{2}}$