If a line makes an angel of `pi/4` with the positive direction of each of x-axis and y-axis, then the angel that the line makes with the positive direction of the z-axis is a. `pi/3` b. `pi/4` c. `pi/2` d. `pi/6`

Options

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

Answer

c

Explanation

Here `l=cos""(pi)/(4),m=cos""(pi)/(4)`
Let the line make an angle `gamma` with the z-axis. Then `l^(2)+m^(2)+n^(2)=1`
or `cos^(2)""(pi)/(4)+cos^(2)""(pi)/(4)+cos^(2)gamma=1`
or `(1)/(2)+(1)/(2)+cos^(2)gamma=1`
or `2cos^(2)gamma=0orcosgamma=0orgamma=(pi)/(2)`