Given a Tetrahedron $OABC$ such that $O(0,0,0),A(a,0,0),B(0,b,0),C(0,0,c)$ ; $a,b,c$ are not zero.
We build a plane $\pi$ that is parallel to $z$-axis and also to $AB$.
Plane $\pi$ cuts plane $ABC$ on line $l_1$ and also cuts plane $OAB$ on line $l_2$ (inside the Tetrahedron).
We connecting point $O$ with point $N$, which is on line $l_1$, and point $C$ with point $M$, which is on line $l_2$.
$ON$ and $CM$ are intersecting inside the Tetrahedron.
Need to find the locus of all intersecting points of $ON$ ans $CM$ such that $N,M$ are moving on $l_1,l_2$ respectively.
the answer is the plane: $\frac{cx}{a}+\frac{cy}{b}+2z-c=0$ which i don't know why.
I'd glad to see any soultion, it's hard i think.
I tried to use dot product in some way and to use some technique with scalar computation but it didn't work for me.
Thanks.