Question

Vector $\overrightarrow{Q}$ has a magnitude of 8 is added to the vector $\overrightarrow{P}$ which lies along the X-axis. The resultant of these two vectors is a third vector $\overrightarrow{R}$ which lies along the $Y$-axis and has a magnitude twice that of $\overrightarrow{P}$. The magnitude of $\overrightarrow{P}$ is:

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

Answer 1

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

Let the $\overrightarrow{P}$ be $x\hat{i}$ . Then the $\overrightarrow{Q}$ has to be $-x\hat{i}+2x\hat{j}$ to make the resultant vector in y - direction and double the magnitude of $\overrightarrow{P}$.

Now, magnitude of $\overrightarrow{P}$ is x.

Using $\sqrt{(x^2+4x^2)}$ = 8 (here magnitude of $\overrightarrow{Q}$ is 8)
=>$x=\frac{8}{\sqrt{5}}$