# Cross product and coordinate systems

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I'm a little confused about cross product and left/right coordinate systems. Consider these two vectors: A = {0, 0, 1} B = {1, 0, 0} Without considering coordinate systems, the cross product is {0,1,0}. Now in a left handed system, I get {0, -1, 0} following the right hand rule, but {0,1,0} using a left hand rule. This is obviously a basic question, but I'm not quite sure how to interpret this. How can I use this information to build a look at camera matrix in the two different coordinate systems? Thanks for any info.

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When you represent the vectors with numbers, you always have some a reference coordinate system (basis). The numerical result has the meaning only in the same basis. In the left-handed system the cross product is still {0,1,0} but the basis is now different and the three numbers correspond to some other vector.

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