Plane through origin perpendicular to another plane?

[Azndoode1]

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]

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>?

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]

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.

How do you find a perpendicular plane though?

 

[Dick]

How do you find a perpendicular plane though?

Two planes are perpendicular if their normals are perpendicular. Find a vector that is perpendicular to <2,3,1>. Any one. There are lots of them. Use that as your normal for the new plane.