Question

Find the angle between two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with magnitudes $1$ and $2$ respectively and when $\overrightarrow{a}.\overrightarrow{b}=1$

Answer 1

It is given that $\overrightarrow{a}.\overrightarrow{b}=1$ and $\left|\begin{array}{c}\overrightarrow{a}\end{array}\right|=1,\left|\begin{array}{c}\overrightarrow{b}\end{array}\right|=2$
The ange between two vectors is
$\cos \theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|\begin{array}{c}\overrightarrow{a}\end{array}\right|\left|\begin{array}{c}\overrightarrow{b}\end{array}\right|}$
$\cos \theta =\frac{1}{12}=\frac{1}{2}$
$\cos \theta =\cos \frac{\pi }{3}$
$\theta =\frac{\pi }{3}$

Final answer:
Hence, the angle between the two vectors is $\frac{\pi }{3}$.