Question

A vector $\overrightarrow{B}$ which has magnitude 8 is added to a vector $\overrightarrow{A}$ which lies along the x-axis. the sum of their two vectors is a third vector which lies along the y-axis and has a magnitude that is twice the magnitude of $\overrightarrow{A}$. Find the magnitude of $\overrightarrow{A}$

Answer 1

Given,

A $\overrightarrow{B}$ having magnitude $8$

So,

Let unit vector along x and y axes by i and j respectively,

$A/Q$

$8+Ai=2Aj$

$8=2Aj-Ai$

$8=\sqrt{(2A{)}^2+A^2)}$

$8=\sqrt{5A^2}$

$8=A\sqrt{5}$

$A=\frac{8}{\sqrt{5}}$

Thus, the magnitude of $\overrightarrow{A}$ is $\frac{8}{\sqrt{5}}$