A line AB in three-dimensional space makes angles `45^(@) and 120^(@)` with the positive X-axis and The positive Y-axis, respectively. If AB makes an acute angle`theta` with the positive Z-axis, then `theta` equals

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^(@)`