If a line makes angle `pi/3\ a n d\ pi/4` with x-axis and y-axis respectively, then the angle made by the line with z-axis is `pi//2` b. `pi//3` c. `pi//4` d. `5pi//12`

Options

A. `(pi)/2`
B. `(pi)/3`
C. `(pi)/4`
D. `(5pi)/12`

Answer

B

Explanation

We have `alpha=(pi)/3,beta=(pi)/4`
`:.l="cos"(pi)/3=1/2, m="cos"(pi)/4=1/(sqrt(2))`
Suppose the line makes angle `gamma` with z-axis and has direction cosines `l,m,n`. Then,
`l^(2)+m^(2)+n^(2)=1`
`implies1/4+1/2+n^(2)=1impliesn=+-1/2impliescos gamma=+-1/2impliesgamma=(pi)/3` or `(2pi)/3`