Application of vector method How to use vector to show plane parallel

Application of vector method How to use vector to show plane parallel

The plane is perpendicular, that is to say, the line is the normal vector of the plane. Of course, the unit normal vector is parallel to the line, but the discussion with the 0 vector should be excluded. The 0 vector is parallel to any vector, but the 0 vector is not perpendicular to the plane
For example, the unit normal vector is (x, y, z) and the direction vector of the line is m = (a, B, c)
So m = a (x, y, z), which is not quite right
For example, if the unit normal vector is (0,1,0), is m = 0?
It can only be a ≠ 0
Plane parallel: it can be proved that the normal vectors of two planes are parallel
But it's not necessarily the unit normal vector. The unit normal vector is the normal vector whose module is equal to 1. In fact, we only need to prove that the normal vectors of two planes are perpendicular
Of course, you have to prove that the lines parallel to the two planes are parallel,
Or a line parallel to one plane is perpendicular to the normal vector of another plane