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mathgraphics3dcoordinate-systemscross-product

Does the method for computing the cross-product change for left handed coordinates?

Does the method for computing the cross-product change for left handed coordinates?

Solution

  • The formula for the cross product of the vectors (x1, x2, x3) and (y1, y2, y3) is

    z1 = x2 * y3 - x3 * y2
z2 = x3 * y1 - x1 * y3
z3 = x1 * y2 - x2 * y1

    It is designed in a way that the three vectors x, y and z in the given order have the same handedness as the coordinate system itself. This property does not depend on the handedness of the coordinate system -- for a left-handed coordinate system the vectors fulfil the left-hand rule. You don't need to change anything about the formula.

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