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**Whiskyfied** i have two equations of two planes that intersect at the origin:

$\displaystyle $ax + by + cz = 0$ $

and

$\displaystyle $dx + ey + fz = 0$ $

as I have three variables, $\displaystyle $x, y, z$$ 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 $\displaystyle $\lambda$$ such that $\displaystyle $a = \lambda d $$ ; $\displaystyle $b = \lambda e $$ ; $\displaystyle $c = \lambda f $$then the same line, i.e. the points whose co-ordinates satisfy $\displaystyle $dx + ey + fz = 0$$ also satisfy $\displaystyle $\lambda adx + \lambda ey + \lambda fz = 0$$that is: $\displaystyle $ax + by + cz = 0$$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!