look, in 2d what you need to do is that if you have function:
PointInside(x,y,x1,y1,x2,y2,x3,y3) then you need to calculate the area of the triangles: (x,y)(x1,y1)(x2,y2) , (x,y)(x2,y2)(x3,y3) , (x,y)(x1,y1)(x3,y3) and if it equals to the area of (x1,y1)(x2,y2)(x3,y3) you can be sure it is inside the triangle. I'm tired and going to sleep, so I would look tomorrow if no one will answer you how to implement it in 3d.
PointInside(x,y,x1,y1,x2,y2,x3,y3) then you need to calculate the area of the triangles: (x,y)(x1,y1)(x2,y2) , (x,y)(x2,y2)(x3,y3) , (x,y)(x1,y1)(x3,y3) and if it equals to the area of (x1,y1)(x2,y2)(x3,y3) you can be sure it is inside the triangle. I'm tired and going to sleep, so I would look tomorrow if no one will answer you how to implement it in 3d.