i have two equations of two planes that intersect at the origin:
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!
(I've tried solving simultaneously: multiplying the first equation through by d; finding y in terms of z, then x in terms of z... and then substituting back into the original equations, but everything cancels out to produce !
i think this means that the equation of the line is calculated by the determinant of
where not all a, b, c or x, y, z are zero
if I'm wrong, please tell me! (sorry about the breaking space notation - don't know how to get rid of it!)
thanks everso for your help!