JEE Mains · Physics · STD 11 - Vectors
- JEE Mains 2024
- Hard
- MCQ
If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(\mathrm{R}\) are inclined at an angle \(\theta\), then...
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=2 \mathrm{R} \cos \left(\frac{\theta}{2}\right)\)
Step-by-step Solution
Detailed explanation
The magnitude of resultant vector
\(R^{\prime}=\sqrt{a^2+b^2+2 a b \cos \theta}\)
Here \(a=b=R\)
Then \(R^{\prime}=\sqrt{R^2+R^2+2 R^2 \cos \theta}\)
\(=R \sqrt{2} \sqrt{1+\cos \theta}\)
\(=\sqrt{2} R \sqrt{2 \cos ^2 \frac{\theta}{2}}\)
\(=2 R \cos \frac{\theta}{2}\)
\(R^{\prime}=\sqrt{a^2+b^2+2 a b \cos \theta}\)
Here \(a=b=R\)
Then \(R^{\prime}=\sqrt{R^2+R^2+2 R^2 \cos \theta}\)
\(=R \sqrt{2} \sqrt{1+\cos \theta}\)
\(=\sqrt{2} R \sqrt{2 \cos ^2 \frac{\theta}{2}}\)
\(=2 R \cos \frac{\theta}{2}\)
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