Question

Three forces $A,B$ and $C$ acting at a point are in equilibrium. The ratio of angles between $A$ and $B$; $B$ and $C$; and $A$ and $C$ is $1:2:3$. Then, $A:B:C$ is

• A. $1:\frac{\sqrt{3}}{2}:\frac{1}{2}$
• B. $\frac{1}{2}:\frac{\sqrt{3}}{2}:1$
• C. $1:\frac{1}{2}:\frac{1}{3}$
• D. $1:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}$
• E. None of these

Answer 1

The correct option is E None of these

Let the angles between $A$ and $B$, $B$ and $C$, $C$ and $A$ is $x,2x$ and $3x$
Thus $x+2x+3x={360}^o$
$\Rightarrow x={60}^o$
By Lamis theorem, we have
$\frac{A}{\sin {120}^o}=\frac{B}{\sin {180}^o}=\frac{C}{\sin {60}^o}$
$\Rightarrow \frac{A}{\frac{\sqrt{3}}{2}}=\frac{B}{0}=\frac{C}{\frac{\sqrt{3}}{2}}$
Therefore, $A:B:C=\frac{\sqrt{3}}{2}:0:\frac{\sqrt{3}}{2}$