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In "Learning OpenCV: Computer Vision with the Opencv" by Gary Bradski, Adrian Kaehler, the authors defined the origin to be center of projection of the left camera, with X positive towards right camera, Y downwards and Z away from camera. Is this right?

Yes this is true and it is also the general rule of applying stereo calibration. Take a look at the following image, which specifies a universal set of parameters that everyone uses for calibration.