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Let a = (1, -2, 1), b = (2, 1, -1), c = (1, 1, 2), d = (3, -1, 2).…
Question
Let a = (1, -2, 1), b = (2, 1, -1), c = (1, 1, 2), d = (3, -1, 2). Compute the squared magnitude |a × (b × (c × d))|^2.
✓ Verified answer: 176checked by our engine — not a guess
Step-by-step solution
Work from the inside out using the vector triple product u × (v × w) = (u·w)v - (u·v)w.
c × d = (1·2 - 2·(-1), 2·3 - 1·2, 1·(-1) - 1·3) = (4, 4, -4).
b × (c × d): with u = b, v = c × d. Use direct cross product: (2,1,-1) × (4,4,-4) = (1·(-4) - (-1)·4, (-1)·4 - 2·(-4), 2·4 - 1·4) = (0, 4, 4).
a × (0, 4, 4) = ((-2)·4 - 1·4, 1·0 - 1·4, 1·4 - (-2)·0) = (-12, -4, 4).
Squared magnitude = 144 + 16 + 16 = 176.
Final answer176
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