Exercise 2: Testing for Parallel Vectors With the Cross Product — Possible Solution
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GIVEN
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g = [2, 4, -2]
h = [-1, -2, 1]

STEP 1: COMPUTING g x h
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  First component:  g2h3 - g3h2 = (4)(1) - (-2)(-2)   = 4 - 4 = 0
  Second component: g3h1 - g1h3 = (-2)(-1) - (2)(1)    = 2 - 2 = 0
  Third component:  g1h2 - g2h1 = (2)(-2) - (4)(-1)    = -4 + 4 = 0

  g x h = [0, 0, 0]

STEP 2: CONCLUSION FROM THE CROSS PRODUCT
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Per this chapter's own parallel-vector test, a cross product of the
zero vector means g and h are parallel (or anti-parallel) - they
point along the same line.

STEP 3: CONFIRMING VIA SCALAR MULTIPLE
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Checking whether h is a scalar multiple of g: dividing each component
of h by the corresponding component of g gives a consistent ratio:

  -1 / 2  = -0.5
  -2 / 4  = -0.5
  1 / -2  = -0.5

Every component gives the same scalar, -0.5, confirming h = -0.5 * g
exactly. Since h is a negative scalar multiple of g, the two vectors
are anti-parallel (same line, opposite direction) - consistent with
the cross product test.

WHY THIS WORKS AS AN ANSWER
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It applies this chapter's own cross-product parallel test directly,
getting the zero vector as the result, and then independently confirms
the conclusion using a completely different method (checking for a
consistent scalar ratio between components) rather than treating the
cross-product test result as unverifiable on its own.