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CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Q21 Marksline_angles

CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Question 2 (Three Dimensional Geometry)

For direction cosines (l₁,m₁,n₁) and (l₂,m₂,n₂), which formula gives the acute angle θ between the lines?

✅ Step-by-Step Solution

Final Answer: cos θ=|l₁l₂+m₁m₂+n₁n₂|
  1. The dot product of the unit directions gives the cosine for the chosen orientations. Its magnitude gives the acute angle regardless of orientation.

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