Can a line have direction angles 45°, 60°, 120°? A. Yes, always B. No, never C. Only if it passes through the origin D. Only in a 2D plane Answer: A) Yes, always Explanation: Check if sum of squares of cosines is 1: cos²(45°) + cos²(60°) + cos²(120°) = (1/√2)² + (1/2)² + (−1/2)² = 1/2 + 1/4 + 1/4 = 1. Yes, it is possible.

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imo class 12 three dimensional geometry

Can a line have direction angles 45°, 60°, 120°?

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#IMO #Class 12 #Mathematics #Three-Dimensional Geometry #logical-reasoning

Can a line have direction angles 45°, 60°, 120°?

A. Yes, always
B. No, never
C. Only if it passes through the origin
D. Only in a 2D plane

Answer: A) Yes, always

Explanation: Check if sum of squares of cosines is 1: cos²(45°) + cos²(60°) + cos²(120°) = (1/√2)² + (1/2)² + (−1/2)² = 1/2 + 1/4 + 1/4 = 1. Yes, it is possible.

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