Revision history [back]

Ok, you take each point one at a time and get your values for a,b,c.

Starting with $ax + by + cz = 4$ and the point $(4,0,0)$, you see that with this point $x=4, y=0$ and $ z=0$.

So we get $a4 +b0 + c0 = 4$

This leaves $4a=4$, so $a=1$.

Now with the point $(0,1,0) x=0, y=1$ and $z=0 $. So we have $by=4$, so $b=4$.

With $(0,0,2)$, $x=0, y=0$ and $z=2$ leaving $cz=4$, so $c=2$.

Now with values for a,b,c, we have the equation for the plane, $x + 4y +2z = 4$.

I never would have thought of doing this and thought it was pretty neat!