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Vector Math, Kinect, 3D World

Devlafford
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I'm programming using the Kinect to interface with a 3D world. I have made it so that the hands control objects in the 3D space; if you move your hand towards the sensor, the objects move in the -Z direction, etc. 

If I rotate the camera, however, it begins to feel unnatural as the objects no longer appear to move in the same direction as the hand. I want to adjust the calculations such that the objects always move on the axis with respect to the camera. To do this, I need to make the z component of the 'change vector' (the vector the objects would move on with respect to the global frame) align with the 'track vector' (the vector between where the camera is and the point it's looking at). How does one rotate a vector such that a given component of it is parallel to another vector? 

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