Asked by Sara

What is the nature of intersection of these three planes:
5x+3y-z=11
-2x-7y+10z=2
6x+21y-30z=-6

I know that the answer is two parallel planes and the other one intersecting in a line. my question is how would you know that the first equation intersects in a line? Would you use elementary operations?

Answered by Sara
correction, the two planes are coincident that the other intersects in line
Answered by Steve
unless the normals are parallel, the planes must intersect in a line.
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