The problem involves finding a plane that passes through the origin and is perpendicular to another given plane defined by the equation M: 2x + 3y + z = 12. Participants are exploring the conditions for perpendicularity between planes and the implications of normal vectors.
The discussion is ongoing, with participants sharing insights about the relationship between the normals of the planes. Some guidance has been provided regarding the selection of a normal vector for the new plane, but there is still uncertainty about the process of finding a perpendicular plane.
Participants express a lack of clarity on how to proceed with the problem, indicating that they are grappling with the concepts involved and the requirements for the planes in question.
Azndoode1 said:Homework Statement
Find a plane through the origin that meets the plane M : 2x + 3y + z = 12 in a right angle. How do you know your plane is perpendicular to M?
Homework Equations
Honestly have no idea... I know how to find an equation for a plane given a normal and a point, however.
The Attempt at a Solution
All I really know is that the normal of M, which is the perpendicular vector, would be <2,3,1>?
Dick said:Call your plane N. Then you want the normal of N to be perpendicular to the normal of M. There's a lot of choices that work. Pick one. Now it also has to pass through the origin. Now since you how to find an equation for a plane given a normal and a point, you should be done.
Azndoode1 said:How do you find a perpendicular plane though?