A line AB in three-dimensional space makes angles 45° and 120°

• 3D Geometry

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 θ with the positive z-axis, then θ equals

1. 30°
2. 45°
3. 60°
4. 75°

Answer

cos² a + cos² b + cos² c = 1

a = 45°

b = 120°

c = θ

1/2 + 1/4 = 1 - cos² θ

3/4 = sin² θ

sin θ = (√3/2)

The correct option is C.