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Triangle intersection in 3D

Problem

Triangle A, B, C is defined by three points:
A=(4,2,4)B=(5,5,5)C=(3,2,6)\begin{aligned} A &= (4, 2, 4) \\ B &= (5, -5, 5) \\ C &= (3, -2, 6) \\ \end{aligned}
A ray intersects the plane defined by A, B, C at a point, I.
If I, equals, left parenthesis, 3, point, 1, comma, minus, 4, point, 3, comma, 4, point, 9, right parenthesis, is I inside triangle, A, B, C?
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