Lucia has $600 in her checking account. She wants to spend part of this money on a computer. She wants to have exactly $250 left
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The volume is the scalar triple product of the direction vectors from the first point to the others. That is computed as the magnitude of the determinant of the matrix of vector values.
a = (-1, -12, 4) - (5, -5, -1) = (-6, -7, 5)
b = (11, -9, -3) - (5, -5, -1) = (6, -4, -2)
c = (0, 2, -3) - (5, -5, -1) = (-5, 7, -2)
Then |(a×b)•c| is
The volume is 176 cubic units.