If be the angle between the unit vectors a and b, then 2 = - Vidyadip

MCQ

If $\theta$ be the angle between the unit vectors $ a$ and $b$, then $\cos \frac{\theta }{2} = $

A
$\frac{1}{2}\,|a - b|$
✓
$\frac{1}{2}\,|a + b|$
C
$\frac{{|a - b|}}{{|a + b|}}$
D
$\frac{{|a + b|}}{{|a - b|}}$

✓

Answer

Correct option: B.

$\frac{1}{2}\,|a + b|$

b
(b) $(a + b).(a + b) = \,|a{|^2} + |b{|^2} + \,2a\,.\,b$

or $|a + b{|^2} = 2.2{\cos ^2}\frac{\theta }{2} \Rightarrow \cos \frac{\theta }{2} = \frac{1}{2}|a + b|.$

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