If a unit vector ` vec a` makes angle `pi//4` with ` hat i ,pi//3` with ` hat j` and an acute angle `theta` with ` hat k` , then find the components of ` vec a` and the angle `thetadot`

Explanation

unit vector `vec a have (a_{1}, a_{2}, vec a_{1})` components.


`
vec a=a_{1} hat{i}+a_{-} hat{j}+a_{hat{k}}`



Also, it is given that `vec a` makes angles `frac{pi}{3}` with `hat{i}, frac{pi}{4}` with `hat{j},` and an acute angle theta with `hat{k}`


`cos frac{pi}{3}=frac{2}{|vec a|} `

`
=frac{1}{2}=2,[|x|=1]`


`cos frac{pi}{4}=frac{2}{|vec a|} `

`
...