# Intersect of Surface and Line in 3D Space

Attached, find a graphic of a Plane and a Line.

I'm hoping the solution can be conveyed without Matrix math, and am thinking it ought to be solvable using 'conventional' simutaneous equations (which I almost 'get').

Too, I'm hoping the solution will be fairly 'general', in the sense that, after understanding this first effort, that I will be able to apply it to a more complex surface.

THANKS!

https://brainmass.com/math/intersect-surface-line-space-16314

#### Solution Preview

Hello,

I appreciate your work in visualizing the plane and line in space and obtaining the approximate point of intersection.

In the attached file, I have explained the complete procedure (substitution method, not matrix method)of obtaining the required point of intersection. I hope you can understand this.

Well. The solutions can be obtained using a simple substitution method.

I appreciate your work in getting ...

#### Solution Summary

A solution to the intersect of a line and a surface is found using a substitution method.