Question

The magnitude of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are 3 and 2 respectively. Find the angle between them if their dot product is equal to 10.

Answer 1

Given that,

The magnitude of $|\overrightarrow{A}|=5$

The magnitude of $|\overrightarrow{B}|=2$

The dot product of the vectors $=10$

We know that,

$\overrightarrow{A}\cdot \overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\cos \theta$

$\cos \theta =\frac{10}{3\times 2}$

$\theta ={\cos }^{-1}\left(\frac{5}{3}\right)$

Hence, the angle is ${\cos }^{-1}\left(\frac{5}{3}\right)$