For the Mathematically Inclined

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:

  1. math_a
  2. math_b
  3. math_c
  4. 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:

math_diagram

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.

Category(s): Pseudorandom
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