I got confused by your answer as in the book there's a question with this answer:
Find the equation of the plane perpendicular to -1 + 3j + 2k and passing through the point (1,0,4):
-(x-1) + 3(y-0) + 2(z-4) = 0
which is the same way you approach the parallel problem... can you explain this to me?
If you are looking for a plane perpendicular to a given plane, then there are an infinite number of those planes. Example: Open a door. Normally the door is perpendicular to the floor, but there isn't only one position the door can have.
If you have a vector ( )and a point Q with its stationary vector you can derive the equation of a plane which is perpendicular to the vector and contains the given point: Let R denote an arbitrary point in the plane with its stationary vector . Then the vector must be perpendicular to the vector . That means: For all points in the plane the equationand the example from the book that I present ask for perpendicular, and you solve both the same way.. why is that?
is true and therefore this equation describes the plane completely (Point-normal-form of the equation of a plane)