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Compute the scalar triple product of given vectors

by RoRi

For each of the following sets of vectors A,B,C compute the scalar triple product.

  1. A = (3,0,0), \qquad B = (0,4,0), \qquad C = (0,0,8).
  2. A = (2,3,-1), \qquad B = (3,-7,5), \qquad C = (1,-5,2).
  3. A = (2,1,3), \qquad B = (-3,0,6), \qquad C = (4,5,-1).
  1. We compute

        \[ [ABC] = A \cdot B \times C = (3,0,0) \cdot (32,0,0) = 96+0+0 = 96. \]

  2. We compute

        \[ [ABC] = A \cdot B \times C = (2,3,-1) \cdot (11,-1,-8) = 2(11) + 3(-1) + (-1)(-8)= 27. \]

  3. We compute

        \[ [ABC] = A \cdot B \times C = (2,1,3) \cdot (-30,21,-15) = -60 + 21 - 45 = -84. \]

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