Find the value of the parameter α for which the pencil of planes through the straight line AB has a common plane with the pencil of planes through the straight line CD, where A(1, 2α, α), B(3, 2, 1), C(−α, 0, α) and D(−1, 3, −3).
Let Δ be a line given by two equations:
The collection of all planes containing a given straight line Δ is called the pencil of planes through Δ.
The plane π belongs to the pencil of planes through the line Δ if and only if there exists λ,μ∈ℝ such that the equation of the plane π is:
The Attempt at a Solution
I wrote the equations of the lines AB and CD. But I don't know the condition for a plane to be common to two pencil of planes in the same time.