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.
`:.cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
Here, `alpha=120^(@)` and `gamma=60^(@)`
`:.cos^(2)120^(@)+cos^(2)beta+cos^(2)60^(@)=1`
`rArr (1/2)^(2)+cos^(2)beta+(1/2)^(2)=1`
`rArr cos^(2)beta=1-(1)/(2)=(1)/(2)`
`rArr cos beta=(pm1)/(sqrt(2))`
`rArr beta=135^(@)`