If a line makes angle `120^(@) and 60^(@)` with the positive directions of X and Z-axes respectively, then the angle made by theline with positive Y-axis is

Options

A. `150^(@)`
B. `60^(@)`
C. `135^(@)`
D. `120^(@)`

Answer

C

Explanation

Let angles `alpha,beta,gamma` makes positive direction of X,Y and Z-axes, respectively.
`thereforecos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
Here, `alpha=120^(@) and gamma=60^(@)`
`thereforecos^(2)120^(@)+cos^(2)beta+cos^(2)60^(@)=1`
`implies((1)/(2))^(2)+cos^(2)beta+((1)/(2))^(2)=1`
`impliescos^(2)beta=1-(1)/(2)=(1)/(2)`
`impliescosbeta=(+-(1))/(sqrt(2))`
`impliesbeta=135^(@)`