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Definition: The cross product of u = [u_1, u_2, u_3] and v = [v_1, v_2, v_3] is the vector u X v defined by u X v = [(u_2)(v_3) – (u_3)(v_2), (u_3)(v_1) – (u_1)(v_3), (u_1)(v_2) – (u_2)(v_1)].
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)