Linear Algebra (line perpendicular to plane)

[thepillow]

Hey all,

I have a 2-flat in R⁴ defined parametrically by:



I'm trying to find a 1-flat, i.e. a line, perpendicular to the plane. Could I write the equation of such a line like this:



My thinking is that I can just keep the initial point, [1,1,1,1], the same and then multiply one of my parameters by a normal vector to the vectors in my initial equation.

Does this work?

Thanks in advance for your help, I really appreciate it!

 

[daon2]

You can choose any point you want. (1,1,1,1) is fine, but why not (0,0,0,0)? To see if your choice is correct, take a dot product of the line's direction vector with an arbitrary vector in your plane?

 

[HallsofIvy]

Hey all,

I have a 2-flat in R⁴ defined parametrically by:

View attachment 2225

I'm trying to find a 1-flat, i.e. a line, perpendicular to the plane. Could I write the equation of such a line like this:

View attachment 2226

My thinking is that I can just keep the initial point, [1,1,1,1], the same and then multiply one of my parameters by a normal vector to the vectors in my initial equation.

Does this work?

Thanks in advance for your help, I really appreciate it!

But it's probably not a good idea to to use "p" as parameter when it is already being used for the plane- use "t" instead.