Find the angles made by `veca=3hati-6hatj+2hat k` with the coordinate axes (standard basis vectors).
Any vector in 3-D can be written as

Explanation

Any vector in 3-D can be written as
`vecr=rcos alpha hati + r cos betahatj + r cos gammahatk …(i)`
`veca=3hati-6hatj+2hat k` … (ii)
Comparing (i) and (ii)
`cos alpha =3/r, cos beta =-6/r, cos gamma =2/r`
`r = sqrt(9+36+4)=7`
`cos alpha = 3/7, cos beta =(-6)/7 cos gamma =2/7`
angle with X, Y and Z axis are respectively
`alpha = cos^(-1)(3/7), beta cos ^(-1) ((-6)/7), gamma =cos^(-1)(2/7)`