This relates to the cross product. There is a way to determine the direction of the cross product of two vectors, using the "right hand rule" - in short, to determine the direction of (A cross B), you orient your right hand such that you can sweep your fingers from A to B. Your thumb will point in the direction of the cross product. Google "cross product - right hand rule" for better pictures and explanations. But you could redefine the cross product by using your left hand - this will just reverse the direction of the resulting vector.
you can determine the Z vector of your coordinate system by taking the cross product of the X and Y vectors (or in other language, get the k vector by taking the cross product of the i and j vectors). If you find the z direction by using a right handed cross product of x and y, its a right handed coordinate system. Likewise for a left handed cross product, and left handed coordinate system.
Hope that makes sense. But in short, the z vector is reversed.