How can you determine the parallelism of two planes?

Does the result in number 6 have to be parallel? But in b), that's not the case, because there's another point that passes through the plane. How do you recognize the parallelism then? By the coefficients?

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Willy1729
7 months ago

Hello,

E2 and E4 are parallel, because the numbers before x1, x2 and x3 of E4 will get you when you multiply those of E2 with (-1).

Since the -1 also emerges from the 1, the planes are even the same.

If you find a parallel to a level ax+by+cz=d, you simply retain a, b and c and take a different value for d than before.

If the parallel is to go through a point (x|y|z), you enter the point into the level equation and calculate d.

Best regards,

Willy

gauss58
7 months ago

By means of the coefficients a, b and c of the coordinate form, you can form the normal vectors. If the normal vectors of two planes are collinear to one another, the two planes are parallel.