How do I decide if a point is within the triangle

[Asuralm]

Hi all:
Give three point P1, P2, P3 in R^3. How do I decide if a point P is inside of the triangle P1P2P3 please?

 

[morphism]

P1, P2, and P3, provided that they aren't colinear, determine a plane. So the first condition is that P lies in that plane. Then it becomes a problem in R^2.