A line AB in three-dimensional space makes angles `45oa n d""120o` with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle q with the positive z-axis, then q equals (1) `45o` (2) `60o` (3) `75o` (4) `30o`

Options

A. `60^(@)`
B. `75^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

A

Explanation

We have
`l=cos 45^(@)=1/(sqrt(2)),m =cos 120^(@)=-1/2` and `n=cos theta`
`:.l^(2)+m^(2)+n^(2)=1`
`implies1/2+1/4+cos^(2) theta=1impliescos^(2)=1/4impliescos theta1/2 [ :' theta "is acute"]`
`impliestheta=60^(@)`