I was comparing the areas of a triangle that could be obtained via the conventional method, dot product, and cross product. Strangely, the latter did not agree with the former two.
Consider two vectors, A <1,1,1> and B<1,1,0>. Both these vectors form a right angled triangle with an angle of 45deg between both vectors, a hypotenuse of SQRT(3), and length of SQRT(2).

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