JEE Main 2024 Mathematics question
Let P(x, y, z) be a point in the first octant, whose projection in the xy-plane is the point Q. Let OP = γ; the angle between OQ and the positive x-axis be θ; and the angle between OP and the positive z-axis be φ, where O is the origin. Then the distance of P from the x-axis is:
Answer: (A)
Solution
z = γcos φ, OQ = γ sin φ and y = γ sin φ sin θ. The distance from the x-axis is √(y² + z²) = γ√(sin²φ sin²θ + cos²φ) = γ√(1 − sin²φ cos²θ).