Question

(Linear Algebra):
1. Why is N*(P0P) called the point-normal form for the plane? Aren't these just two orthogonal vectors, that do not describe a plane?

2. Is the dot product of N and P0P always = 0 as they are orthogonal?

Answer 1

i believe 1 represents the normal being dotted to group of vectors, and all the vectors that equate to a dot of zero are perp to the normal; all those vectors create a plane

Answer 2

spose we have some point A: (x,y,x) and some other point B:(xo,yo,zo)

any vector from B to A is defined as <x-xo, y-yo,z-zo>, the set of these vectors creates a space in R^3

if we have another vector N:<a,b,c> and want to know all the vectors that are perp to it; we dot it with our R^3 set

<a,b,c> . <x-xo,y-yo,z-zo> = 0

a(x-xo) + b(y-yo) + c(z-zo) = 0

Answer 3

@amistre64 you have just explained this more clearly to me than 2 textbooks. Huge relief! Thanks!