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

- 30°
- 45°
- 60°
- 75°

**Answer**

cos^{2} a + cos^{2} b + cos^{2} c = 1

a = 45°

b = 120°

c = θ

1/2 + 1/4 = 1 - cos^{2} θ

3/4 = sin^{2} θ

sin θ = (√3/2)

**The correct option is C.**