QJEEM24Ph542a: JEE Main 2024 Physics - Class 11 JEEM24Ph542a Solution: If two vectors and having equal magnitude are inclined at angle …

Question

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If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $R$ are inclined at angle $\theta$ , then

Accepted Answer

The magnitude of resultant vector

$R^{\prime}=\sqrt{a^2+b^2+2 a b \cos \theta}$

Here $a=b=R$

Then $R^{\prime}=\sqrt{R^2+R^2+2 R^2 \cos \theta}$

$\begin{aligned}& =R \sqrt{2} \sqrt{1+\cos \theta} \\& =\sqrt{2} R \sqrt{2 \cos ^2 \frac{\theta}{2}} \\& =2 R \cos \frac{\theta}{2}\end{aligned}$

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