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How to Find the Equation of a Plane From Two Lines

If we have two lines in 3-D space,
z = a*x + c
z = b*y + d
How do I find the plane that passes through those lines?
POSTED BY: Onur Cagirici
2 Replies
Posted 10 years ago
Hi Onur,
Yes, those are each an equation for a line in 2-D space.
If you mean for equation 1 to define a line in the X-Z plane, then you must also require y=0.
If you mean equation 2 to define a line in the Y-Z plane then x=0 is required.
In 3-space, two lines may or may not lie in the same plane. In linear algebra, they lie in the same plane iff there is an R3->R2 projection operator which leaves both lines unchanged.
POSTED BY: David Keith
1. Your equations define planes, not lines.

2. Generically lines with independent coefficients are skew.
POSTED BY: Michael Rogers
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