A line makes angle θ with the x-axis, and angle φ with the y-axis. What angle does it make with the z-axis if θ = φ = 60°? A. 45° or 135° B. 60° or 120° C. 30° or 150° D. 0° Answer: A) 45° or 135° Explanation: cos²60° + cos²60° + cos²γ = 1. 1/4 + 1/4 + cos²γ = 1 → 1/2 + cos²γ = 1 → cos²γ = 1/2. cos γ = ±1/√2. So γ = 45° or 135°.

imo class 12 three dimensional geometry

A line makes angle θ with the x-axis, and angle φ with the y-axis. What angle does it make with the z-axis if θ = φ = 60°?

VAVidaara Admin Asked 6d ago 0 views 0 answers

A line makes angle θ with the x-axis, and angle φ with the y-axis. What angle does it make with the z-axis if θ = φ = 60°?

Answer: A) 45° or 135°

Explanation: cos²60° + cos²60° + cos²γ = 1. 1/4 + 1/4 + cos²γ = 1 → 1/2 + cos²γ = 1 → cos²γ = 1/2. cos γ = ±1/√2. So γ = 45° or 135°.