About finding points in a plane given its normal equation.

Question

$$A: x - y + 2z = 10$$

This describes all the points that belong to the plane $A$, right?

So any triplet $(x,y,z)$ that fulfils the equation is a valid point?

$$R = (10,0,0)\\ S = (0,-10,0)\\ T = (0,0,5)$$

Are all valid? I ask this because, at some point, somebody noted that when "guessing" plane points, I should avoid using so many zeroes. However I can't recall why.

Answer 1

Yes.

I ask this because, at some point, somebody noted that when "guessing" plane points, I should avoid using so many zeroes.

Can't think of why. May be it affected the particular application.