Given points P_1 (2, -1, 4), P_2 (-1, 0, 3), P_3 (4, 3, 1), and P_4(3, -5, 0) fi

Question

Given points P_1 (2, -1, 4), P_2 (-1, 0, 3), P_3 (4, 3, 1), and P_4(3, -5, 0) find the volume of P_1 P_2 P_3 P_4 (a tetrahedron).
--- My work: A = P_2 - P_1 = (-3, 1, -1) B = P_3 - P_1 = (2, 4, -3) C = P_4 - P_1 = (1, -4, -4)
Then the triple product |-3 1 -1| |2 4 -3| |1 -4 4| = -11
The answer should be 101/6 Please help! What am I doing wrong? find the volume of P_1 P_2 P_3 P_4 (a tetrahedron).
--- My work: A = P_2 - P_1 = (-3, 1, -1) B = P_3 - P_1 = (2, 4, -3) C = P_4 - P_1 = (1, -4, -4)
Then the triple product |-3 1 -1| |2 4 -3| |1 -4 4| = -11
The answer should be 101/6 Please help! What am I doing wrong?

Explanation / Answer

Why can you take the absolute value? If it is left handed or something couldn't it be considered in a sense, negative?

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