If |a ,. ,b| , = 3 and |a b| , = 4, then the angle between a and … - Vidyadip

MCQ

If $|a\,.\,b|\, = 3$ and $|a \times b|\, = 4,$ then the angle between $a $ and $ b$ is

A
${\cos ^{ - 1}}\frac{3}{4}$
✓
${\cos ^{ - 1}}\frac{3}{5}$
C
${\cos ^{ - 1}}\frac{4}{5}$
D
$\frac{\pi }{4}$

✓

Answer

Correct option: B.

${\cos ^{ - 1}}\frac{3}{5}$

b
(b) $|a.b| = ab\cos \theta = 3$…..$(i)$

and $|a \times b| = ab\,\sin \theta = 4$…..$(ii)$

Dividing $(ii)$ by $(i),$

we get $\tan \theta = \frac{4}{3} \Rightarrow \cos \theta = \frac{3}{5} \Rightarrow \theta = {\cos ^{ - 1}}\frac{3}{5}.$

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