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?
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
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.