Find the point of intersection of AB and `A(` 6,-7,0),B(16,-19,-4,) , C(0,3,-6) and D(2,-5,10).

Explanation

Let AB and CD intersect at P.
Let P divides AB in ratio `lamda:1` and CD in ratio `mu:1`.
Then coordinates of P are `((16lamda+6)/(lamda+1), (-19lamda-7)/(lamda+1), (-4lamda)/(lamda+1))or ((2mu)/(mu+1), (-5mu+3)/(mu+1), (10mu-6)/(mu+1))`
Comparing we have `lamda=-(1)/(3) or mu=1`.
Using these values, we get point of intersection as (1, -1, 2).
Here it is also proved that lines AB and CD intersect of points A, B, C and D are coplanar.