Thread: 2 dimensional plane in four dimensions

In R4 find the equation of the 2 dimensional plane that passes through the point (0,1,1,-2) and is normal to the vectors N = (2, -1, 0, 1) and M = (0, -1, 3, 0).

I know that you can define a plane as (P-v).N = 0 and (P-v).M=0. What do I have to do in this case?

Originally Posted by TTim

In R4 find the equation of the 2 dimensional plane that passes through the point (0,1,1,-2) and is normal to the vectors N = (2, -1, 0, 1) and M = (0, -1, 3, 0).

I know that you can define a plane as (P-v).N = 0 and (P-v).M=0. What do I have to do in this case?

choose any point on the plane and let then and we want to have which

gives us: thus hence the vector equation of the 2-dimensional plane that you're looking for is:

where are any real numbers.