Line intersection in 3D

Question

I have 4 points. Only three are known:

$P1(a,b,c)$ $P2(x,y,z)$

$P3(d,e,f)$

$P4(g,h,i)$

$L1=(P1P2)$, $L2=(P2P3)$ and $L3=(P3P4)$ are lines. $L1$ and $L2$ intersect with each other at point $P2$. $L2$ and $L3$ intersect with each other at point $P3$.

Length of the lines are also known as:

$L1=K$

$L2=L$

$L3=M$

On the other hand, plane's equations which contain $L1$ and $L3$ are also known.

I would like to know $x,y,z$ intersection point of $L1$ and $L2$.

Thanks in advance. If there is any misinformation in order to be able to slove the problem, please let me know.

Answer 1

Isn't there any solution related this topic. This is a mechanism and every line is an arm of the mechanism. I need to find every position of the mechanism related to motion.