Question

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ of equal magnitude $2\text{unit}$ are at an angle of ${60}^{\circ }$ to each other. Find the ratio of |$\overrightarrow{a}+\overrightarrow{b}$| and |$\overrightarrow{a}-\overrightarrow{b}$|

• A. $\sqrt{3}$
• B. $2$
• C. $3$
• D. $\sqrt{5}$

Answer 1

The correct option is A $\sqrt{3}$


Part $1$
Applying parallelogram law of vector addition
|$\overrightarrow{a}+\overrightarrow{b}$| =$\sqrt{2^2+2^2+2\times 2\times 2\times \cos {60}^{\circ }}$
$\Rightarrow 2\sqrt{3}$ .......(i)

Part $2$

|$\overrightarrow{a}-\overrightarrow{b}$| =$\sqrt{2^2+2^2+2\times 2\times 2\times \cos {120}^{\circ }}$
$\Rightarrow 2$ .........(ii)

so, required ratio= $\frac{|\overrightarrow{a}+\overrightarrow{b}|}{|\overrightarrow{a}-\overrightarrow{b}|}$=$\frac{2\sqrt{3}}{2}=\sqrt{3}$