Exercise 3: Surface Normal Direction and Winding Order — Possible Solution
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GIVEN
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u = [2, 0, 0]
v = [0, 3, 0]

STEP 1: COMPUTING u x v
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  First component:  u2v3 - u3v2 = (0)(0) - (0)(3) = 0
  Second component: u3v1 - u1v3 = (0)(0) - (2)(0) = 0
  Third component:  u1v2 - u2v1 = (2)(3) - (0)(0) = 6

  u x v = [0, 0, 6]

STEP 2: COMPUTING v x u
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  First component:  v2u3 - v3u2 = (3)(0) - (0)(0) = 0
  Second component: v3u1 - v1u3 = (0)(2) - (0)(0) = 0
  Third component:  v1u2 - v2u1 = (0)(0) - (3)(2) = -6

  v x u = [0, 0, -6]

This confirms this chapter's own anti-commutativity rule directly:
v x u = -(u x v), exactly as [0, 0, -6] is the negation of [0, 0, 6].

WHY THE ORDER FLIPS WHICH SIDE IS "THE FRONT"
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u x v points along the positive z-axis (out of the page, using the
right-hand rule: fingers along u, curling toward v, thumb pointing in
+z). v x u points along the negative z-axis instead - straight into
the page. Both vectors are equally valid, perpendicular, correctly-
computed normals for the exact same flat triangle - the only thing
that changed is which of the two possible corner-listing orders was
used.

A 3D modelling tool that lists this triangle's corners in the order
that produces u x v will treat the +z side as the outward-facing
"front" of the surface - the side that gets lit and rendered, while
the opposite side is culled as invisible backface geometry. Listing
the exact same three corners in the reverse order silently flips which
side is considered the front, without changing the triangle's actual
shape or position at all - purely a consequence of which edge vector
was crossed with which, in what order.

WHY THIS WORKS AS AN ANSWER
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It computes both orderings explicitly rather than asserting the sign
flip, confirms the result matches this chapter's own anti-
commutativity identity, and explains the practical consequence (which
side of a rendered surface is treated as the front) directly in terms
of the right-hand rule rather than asserting the winding-order
connection without justification.