Which of the following is true for lines r = a₁ + λb₁ and r = a₂ + μb₂ being coplanar?
Which of the following is true for lines r = a₁ + λb₁ and r = a₂ + μb₂ being coplanar?
- A. (a₂ − a₁) · (b₁ × b₂) = 0
- B. (a₂ − a₁) × (b₁ × b₂) = 0
- C. a₁ · b₁ = a₂ · b₂
- D. (a₂ + a₁) · (b₁ × b₂) = 0
Answer: A) (a₂ − a₁) · (b₁ × b₂) = 0
Explanation: Two lines are coplanar if the vector connecting their base points (a₂ − a₁) is perpendicular to the normal of the plane containing their direction vectors (b₁ × b₂). This is a scalar triple product.
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