Question

If a unit vector `veca` makes angles `pi/3` with `hati,pi/4` with `hatj` and acute angles θ with ` hatk,` then find the value of θ.

Answer 1

Let `veca=xhati+yhatj+zhatk` be the unit vector 

`therefore x=cospi/3=1/2`

`y=cospi/4=1/sqrt2`

Now

` x^2+y^2+z^2=1`

`(1/2)^2+(1/sqrt2)^2+z^2=1`

`z^2=1-1/4-1/2=1/4`

`z=1/2`

`costheta=1/2`

`theta=pi/3`