MHT CET · Maths · Vector Algebra
If \(\bar{a}\) and \(\overline{\mathrm{b}}\) are unit vectors and \(\theta\) is the angle between them, then \(\tan \theta / 2=\)
- A \(|\bar{a}-\bar{b}|\)
- B \(|\bar{a}+\bar{b}|\)
- C \(\frac{|\bar{a}+\bar{b}|}{|\bar{a}-\bar{b}|}\)
- D \(\frac{|\bar{a}-\bar{b}|}{|\bar{a}+\bar{b}|}\)
Answer & Solution
Correct Answer
(D) \(\frac{|\bar{a}-\bar{b}|}{|\bar{a}+\bar{b}|}\)
Step-by-step Solution
Detailed explanation
\(|\bar{a}-\bar{b}|^2 = |\bar{a}|^2 + |\bar{b}|^2 - 2|\bar{a}||\bar{b}|\cos\theta = 1+1-2\cos\theta = 2(1-\cos\theta) = 4\sin^2(\theta/2)\) \(|\bar{a}-\bar{b}| = 2\sin(\theta/2)\)
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