What is the angle between vectors ` vec a\ a n d\ vec b` with magnitudes 2 and `3` respectively ? Given ` vec adot vec b=sqrt(3)` .

Explanation

Given: `|vec{a}|=2`


Given: `|vec{b}|=sqrt{3} `


Given: `vec{a} cdot vec{b}=sqrt{3}`


`vec{a} cdot vec{b}=|vec{a}||vec{b}| cos theta`


`Rightarrow sqrt{3}=(2)(sqrt{3}) cos theta`


`Rightarrow cos theta=frac{sqrt{3}}{2 sqrt{3}} `


`Rightarrow cos theta=frac{1}{2}`


`Rightarrow theta=cos ^{-1}(frac{1}{2})=frac{pi}{3}`