Question

Three vectors $\overrightarrow{A},\overrightarrow{B}and\overrightarrow{C}$ are as shown in figure. If magnitude of $\overrightarrow{A}$ is 4m and $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=0$, then the magnitude of $\overrightarrow{B}and\overrightarrow{C}$ are respectively

• A. $4m,4m$
• B. $4\sqrt{3}m,4\sqrt{3}m$
• C. $4m,4\sqrt{3}m$
• D. $4\sqrt{3}m,4m$

Answer 1

The correct option is D $4\sqrt{3}m,4m$

Breaking $\overrightarrow{B}$ and $\overrightarrow{C}$ into components we get :

$C\cos {30}^{\circ }=B\sin {30}^{\circ }$ ( As vector sum along $Y$ axis $=0$)

$\Rightarrow C\frac{\sqrt{3}}{2}=B\frac{1}{2}$

$C\sqrt{3}=B\to \left(1\right)$

$C\sin {30}^{\circ }+A=B\cos {30}^{\circ }$ (As vector sum along $X$ axis $=0$)

$\Rightarrow \frac{C}{2}+4=\sqrt{3}C\frac{\sqrt{3}}{2}$ ( using equation $1$ and $A=4m$ )

$\Rightarrow C+8=3C$

$\Rightarrow C=4m$

so $B=4\sqrt{3}m$