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

Answer

C

Explanation

`cos^(2) 45^(@) + cos^(2) 120^(@) + cos^(2) theta=1`
` Rightarrow 1/2 + 1/4 + cos^(2) theta =1`
` Rightarrow cos^(2)theta =1 - 3/4 =1/4`
` Rightarrow cos theta = 1/2 " " (therefore theta` is acute)
` theta = 60^(@)`