I’ve been thinking about the following math problem lately (I occasionally get distracted by such things):
Suppose you have four points in 3D space, a, b, c, and p, where a, b, and c are distinct and non-colinear and their positions are known, and p is the unique point defined by the following:
- p lies in the interior of the triangular prism defined by a, b, and c that is perpendicular to the plane containing a, b, and c.
As an image:
If there is only one point satisfying the above criteria, can it be found without knowing γ? I plan on posting my proof next week Thursday, 2016-02-25.