Finding $X_1$ and $X_2$, the 3D coordinates describing the segment between two skew lines

34 Views Asked by At

Assume you have the coordinates of two detector hits $P_1 (x', y', z')$ and $P_2 (x", y", z")$. How do I get the coordinates of the segment (shortest distance between two skew lines), that is $X1$ and $X_2$ as shown in the attached figure?

Please show all the steps clearly up to $X_1(x,y,z)$ and $X_2(x,y,z)$. The attached image shows the mid point with star, I want to calculate $X_1$ and $X_2$.

enter image description here