alleryTwo lines with direction vectors b₁ and b₂ are parallel if and only if
Ab₁ · b₂ = 0
Bb₁ + b₂ = 0
Cb₁ × b₂ = 0
D|b₁| = |b₂|
Answer & Solution
Correct answer: C. b₁ × b₂ = 0
1. Two non-zero vectors are parallel when one is a scalar multiple of the other.
2. Equivalently, their cross product is the zero vector.
3. So b₁ × b₂ = 0 when the lines are parallel.
4. Option A is the perpendicularity condition, not parallelism.
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.4_
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