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`

Options

A. `(pi)/6`
B. `(pi)/3`
C. `(pi)/4`
D. `(pi)/2`

Answer

D

Explanation

Let `alpha=(pi)/4,beta=(pi)/4`
We know
`cosl^(2)alpha +cos^(2)beta+cos^(2)gamma=1`
`:."cos"^(2)(pi)/4+"cos"^(2)(pi)/4+cos^(2)gamma=1`
`implies1/2+1/2+cos^(2)gamma=1`
`impliescos^(2)gamma=0impliesgamma=(pi)/2`