Question

The equation of the plane passing through the line (x - x₁) /l₁ = (y - y₁) /m₁ = (z - z₁) /n₁

and parallel to the line (x - x₂)/l₂ = (y - y₂)/m₂ = (z - z₂)/n₂ is |(x - x₁, y - y₁, z - z₁), (l₁, m₁, n₁), (l₂, m₂, n₂)| = 0

Answer 1

Let L₁ and L₂ be the given lines and A = (x₁,y₁,z₁) (see Fig.). Let vector n₁ = (l₁, m₁, n₁) and vector n₂ = (l₂,m₂,n₂) so that vector (n₁ x n₂) is perpendicular to the required plane. Now

P(x,y,z) is any point in the plane