Class 12 Three Dimensional Geometry · Mcq Single Correct1 Marksdirection_cosines
Class 12 Maths · Three Dimensional Geometry · Mcq Single Correct #6
A line makes angles θ₁,θ₂,θ₃,θ₄ with the four body diagonals of a cube. Find Σ cos²θᵢ.
✅ Step-by-Step Solution
Final Answer: Option (C): 4/3
- For unit direction (l,m,n), sum the squares of (l+m+n),(l+m−n),(l−m+n),(−l+m+n), then divide by 3. Cross terms cancel, giving 4(l²+m²+n²)/3=4/3.
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