Any m 1 (x 1, y 1, z 1) m2 (x2, y2, z2) on this plane has

a(x 1-x2)+B(y 1-y2)+C(z 1-z2)+(D-D)= 0

That is, (a, b, c) is an arbitrary vector perpendicular to the vector M 1M2 and orthogonal to the plane, of course, it is his normal vector, remember.

therefore

It means that vector α is perpendicular to three normal vectors at the same time, that is, vector α is parallel to three planes at the same time.

Det(G) is equal to 0, then G(alpha)=0 has a non-zero solution and a vector is parallel to three planes at the same time.

It is possible that the three planes of 1 intersect on a line; 2. Three planes form a triangular section tube; 3. Two or three of the three planes are coincident; 4. The two planes are parallel, and the third plane intersects the first two planes.

Det(G) is not equal to 0, so only zero vectors can be parallel to three planes at the same time. Three planes and two quantities are not parallel. Imagine two planes meeting on a line. The third plane intersects with this. Obviously, it can't be parallel, but it can only intersect at one point. namely

Three sides intersect at one point.