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

Answer: (D)

According to condition, $ A+Bi=Rj $ (where, R is the resultant vector)
Also, R=2B
$ \therefore $ $ A+Bi=2Bj $
or $ A=2Bj-Bi $
$ \therefore $ $ {{A}^{2}}=4{{B}^{2}}+{{B}^{2}}=5{{B}^{2}} $
Here, $ A=8 $
$\therefore $ $ 64=5{{B}^{2}} $
$ \Rightarrow $ $ B=\sqrt{\frac{64}{5}}=\frac{8}{\sqrt{5}} $