If |a + b| , , > , ,|a - b|, then the angle between a and b is - Vidyadip

MCQ

If $|a + b|\,\, > \,\,|a - b|,$ then the angle between $ a $ and $b$ is

✓
Acute
B
Obtuse
C
$\frac{\pi }{2}$
D
$\pi $

✓

Answer

Correct option: A.

Acute

a
(a) $|a + b|\, > \,|a - b|$

Squaring both sides, we get

${a^2} + {b^2} + 2a\,.\,b\, > \,{a^2} + {b^2} - 2a\,.\,b$

$\Rightarrow 4a.b > 0$ $ \Rightarrow \cos \theta > 0$ Hence $\theta \, < \,90^\circ $

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