Question

If a line makes an angle of `pi/4` with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is (1) `pi/6` (2) `pi/3` (3) `pi/4` (4) `pi/2`

Answer 1

If`l,m,n`is direction of a line then
`l^2+m^2+n^2=0`
and if line make`(alpha ,beta,gamma)`with Co-ordinate xis
`l=Cosalpha`
`m=Cosbeta`
`n=Cosgamma`
`Cos^2alpha+Cos^2beta+Cos^2gamma=1`
`1/2+1/2+Cos^2gamma=1`
`Cos^2gamma=0`
`gamma=pi/2`
option`2=pi/2`