Question

Two vectors whose magnitudes are in ratio 1:2 gives resultant of magnitude 30. If angle between these two vectors is ${120}^{\circ }$, then the magnitude of two vectors will be

• A. $10\sqrt{3},20\sqrt{3}$
• B. $5\sqrt{3},10\sqrt{3}$
• C. $\sqrt{6},2\sqrt{6}$
• D. $2\sqrt{3},4\sqrt{3}$

Answer 1

The correct option is A $10\sqrt{3},20\sqrt{3}$

Let the magnitude of the two vectors be x and $2x$ then:

Magnitude of resultant $=\sqrt{x^2+(2x{)}^2+4x^2\cos \theta }=30$

Given : $\theta ={120}^o$

$\Rightarrow x\times \sqrt{5+4\left(\frac{-1}{2}\right)}=30(\cos {120}^o=-1/2)$

$\Rightarrow x=\frac{30}{\sqrt{3}}=10\sqrt{3}$

So the magnitudes of the two forces are: $10\sqrt{3}$ and $20\sqrt{3}$.