JEE Mains · Physics · STD 11 - 3.1 vectors
Which of the following relations is true for two unit vectors \(\hat{ A }\) and \(\hat{ B }\) making an angle \(\theta\) to each other\(?\)
- A \(|\hat{ A }+\hat{ B }|=|\hat{ A }-\hat{ B }| \tan \frac{\theta}{2}\)
- B \(|\hat{ A }-\hat{ B }|=|\hat{ A }+\hat{ B }| \tan \frac{\theta}{2}\)
- C \(|\hat{ A }+\hat{ B }|=|\hat{ A }-\hat{ B }| \cos \frac{\theta}{2}\)
- D \(|\overrightarrow{ A }-\hat{ B }|=|\overrightarrow{ A }+\hat{ B }| \cos \frac{\theta}{2}\)
Answer & Solution
Correct Answer
(B) \(|\hat{ A }-\hat{ B }|=|\hat{ A }+\hat{ B }| \tan \frac{\theta}{2}\)
Step-by-step Solution
Detailed explanation
\(|\hat{ A }+\hat{ B }|=\sqrt{|\hat{ A }|^{2}+|\hat{ B }|^{2}+2|\hat{ A } \| \hat{ B }| \cos \theta}\) \(=\sqrt{1+1+2 \cos \theta}\) \(=\sqrt{2(1+\cos \theta)}\) \(=\sqrt{2 \times 2 \cos ^{2} \frac{\theta}{2}}\) \(=2 \cos \frac{\theta}{2}\)…
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