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 $A=2Bj-Bi$
$\therefore$ $A^2=4B^2+B^2=5B^2$
Here, $A=8$
$\therefore$ $64=5B^2$
$\Rightarrow$ $B=\sqrt{\frac{64}{5}}=\frac{8}{\sqrt{5}}$