i have two equations of two planes that intersect at the origin:
and
as I have three variables,
and two equations, then I will have an infinite number of solutions: either they are both the same plane or they intersect in exactly one line.
I need to prove this!
I am able to show what happens if they are the same plane:
If there is a non-zero
such that
;
;
then the same line, i.e. the points whose co-ordinates satisfy
also satisfy
that is:
Thus they are the same plane.
but I'm completely at a loss to prove they intersect in precisely one line - any help very gratefully apprectiated!