Mapping 3D point to cone surface using perpendicular line

[mamort]

Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[mamort]

Thanks for monitoring this problem, I have now found the solution which is achieved by solving simultaneous equations of both straight line functions (m1 and m2) that are perpendicular in the top diagram above. The bottom diagram is NOT how the solution is achieved.