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Two lines r = a₁ + s b₁ and r = a₂ + t b₂ are parallel iff
Ab₁ · b₂ = 0
Ba₁ = a₂
Cb₁ + b₂ = 0
Db₁ × b₂ = 0
Answer & Solution
Correct answer: D. b₁ × b₂ = 0
1. Two lines are parallel iff their direction vectors are collinear.
2. Collinear vectors satisfy b₁ × b₂ = 0.
3. Hence the condition b₁ × b₂ = 0.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 6 "Line and Plane" §6.3_
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