# Normal vector from transformation matrix

as you are probably guessing by the title I'm not a math guy. The program I use for work has matrix which describes the position of a plane in 3d space. The center point of that card / plane can be easily read from the matrix. But the matrix also contains information regarding rotation (which I am guessing is in rad) and scale. I wondered if you could calculate the normal vector for the center point using this matrix data (maybe from the rotation?) to describe the plane.

The next question would be how to calculate the 3d positions of the 4 corner points of a square in this plane given a user set the distance from the center.

Thanks for taking the time explaining. picture of matrix here

• But it's a $4\times 4$ matrix.. – Berci Sep 8 '18 at 20:40
• You should clarify how this transformation represents the position of the object. Presumably, it’s a transformation from some standard position. Apply the matrix to the normal of the plane in this standard position. If this standard normal is a unit vector parallel to one of the coordinate axes, then the transformed normal will just be the corresponding column of your matrix. – amd Sep 8 '18 at 21:19