If vectors ` vec a\ a n d\ vec b\ ` are such that `| vec a|=3,\ | vec b|=2/3a n d\ vec axx vec b` is a unit vector, then write the angle between ` vec a\ a n d\ vec b` .

Explanation

Let assume the angle between` vec{a} and vec{b} is theta`


Given:` vec{a} times vec{b}` is a unit vector.


Therefore`|vec{a} times vec{b}|=1`


`Rightarrow|vec{a}||vec{b}| sin theta=1`

`
Rightarrow 3 times frac{2}{3} times sin theta=1 `


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


`Rightarrow theta=frac{pi}{6}`


Hence, the angle between `vec{a} and vec{b} is frac{pi}{6}`