The angle θ between two lines with direction vectors b₁ and b₂ is give…

Question

The angle θ between two lines with direction vectors b₁ and b₂ is given by

Accepted 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: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.4_

Answer

sin θ = b₁ · b₂ / (|b₁||b₂|)

Answer

tan θ = b₁ × b₂ / (b₁ · b₂)

Answer

cos θ = b₁ × b₂ / (|b₁||b₂|)