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.