Question

The magnitude of a component of $\overrightarrow{A}=3\hat{i}+4\hat{j}$ in the direction of $\overrightarrow{B}=\hat{i}+\hat{j}$ is:

• A. $3$
• B. $\frac{7}{5}$
• C. $\frac{7}{\sqrt{2}}$
• D. $7$

Answer 1

The correct option is C $\frac{7}{\sqrt{2}}$

$\cos \theta =\frac{7}{5\sqrt{2}}\&\left|\overrightarrow{A}\right|=\sqrt{3^2+4^2}=5$
Required component $=\left|\overrightarrow{A}\right|\cos \theta =\frac{7}{\sqrt{2}}$