alleryThe angle θ between two lines with direction vectors b₁ and b₂ is given by
Asin θ = b₁ · b₂ / (|b₁||b₂|)
Bcos θ = b₁ · b₂ / (|b₁||b₂|)
Ctan θ = b₁ × b₂ / (b₁ · b₂)
Dcos θ = b₁ × b₂ / (|b₁||b₂|)
Answer & Solution
Correct answer: B. cos θ = b₁ · b₂ / (|b₁||b₂|)
1. The angle between two lines is the angle between their direction vectors.
2. Recall a · b = |a||b| cos θ for two vectors.
3. So cos θ = (b₁ · b₂) / (|b₁| · |b₂|).
4. Option D uses × instead of ·; option A uses sin instead of cos.
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.4_
Keep practising Vector Algebra and 3D Geometry
Browse all Vector Algebra and 3D Geometry questions for AP Intermediate 2nd Year, or explore more Mathematics topics.
Related questions