Question

The magnitude of two vectors are 3 and 4 units and their product is 6 units. the angle between the vectors is

π/6
π/3
π/2​

Answer 1

Answer:-

A=3

B=4

$\sf \overrightarrow{A}.\overrightarrow{B}=6$

We know that

$\boxed{\sf \overrightarrow{A}.\overrightarrow{B}=ABcos\theta}$

$\\ \rm\longmapsto cos\theta=\dfrac{\overrightarrow{A}.\overrightarrow{B}}{AB}$

$\\ \rm\longmapsto cos\theta=\dfrac{6}{3\times 4}$

$\\ \rm\longmapsto cos\theta=\dfrac{6}{12}$

$\\ \rm\longmapsto cos\theta=\dfrac{1}{2}$

$\\ \rm\longmapsto cos\theta=cos60$

$\\ \rm\longmapsto \theta=60°$

Converting to radian:-

$\\ \rm\longmapsto 60°=\dfrac{\pi}{180}\times 60$

$\\ \rm\longmapsto 60°=\dfrac{\pi}{3}rad$

Hence option b is correct.