Orientation of the Cross Product of 3-vectors

The cross product u→×v→ of vectors u→=[a1a2a3], v→=[b1b2b3] in the Euclidean 3-space is defined as follows (see [1, p. 138] or [3, p. 266]):Algebraic definition. u→×v→=[a2b3−a3b2−(a1b3−a3b1)a1b2−a2...