Mapping 3D point to cone surface using perpendicular line

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mamort
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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.

Diagram of a cone with z-axis and a dashed line tangent to the cone; points a and b mark gradients m1 and m3 and axis values az, az + Δaz, ax and ay. Beside it, red handwritten notes list equations for μ1 and m3, with a second diagram showing the points at μ1 on the axis.
 

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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?
 
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.
 

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