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