Question

If a vector $A$ having a magnitude of $8$ is added to a vector $B$ which lies along x-axis, then the resultant of two vectors lies along y-axis and has magnitude twice that of $B$. The magnitude of $B$ is

• A. $\frac{6}{\sqrt{5}}$
• B. $\frac{12}{\sqrt{5}}$
• C. $\frac{16}{\sqrt{5}}$
• D. $\frac{8}{\sqrt{5}}$

Answer 1

The correct option is D $\frac{8}{\sqrt{5}}$

According to condition
$\overrightarrow{A}+B\hat{i}=R\hat{j}$ (Where $R$ is the resultant vector)
Also $R=2B$
$\therefore$ $\overrightarrow{A}+B\hat{i}=2B\hat{j}$
or $\overrightarrow{A}=2B\hat{j}-B\hat{i}$
$\therefore A^2=4B^2+B^2=5B^2$
Here, $A=8$
$\therefore 64=5B^2$
$\Rightarrow B=\sqrt{\frac{64}{5}}=\frac{8}{\sqrt{5}}$