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in this video were going to talk about how to find the equation of a plane given three points now in order to write the equation of a plane or to define any plane for that matter we need a point on a plane and we need a vector that is perpendicular to the plane and that vector is known as the normal vector now we have three points we could use any one of those three points to define the plane the only thing that were missing is the normal vector now lets say that this is point p even though it may not be the exact location of p but for the sake of simplicity lets say thats p this is q and were going to say this is r vector pq were going to call it vector a vector pr is going to be vector b if we take the cross product of these two vectors it will give us a normal vector that is perpendicular to both vectors a and b and so thats how we could find the normal vector given three points so lets start with a vector a which is vector pq so were going to take point q and subtract it
