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How to find coordinates of screen corner if camera mounted on screen

Hello, My setup is a typical laptop with a built in webcam.

I'm trying to find intersection of a vector seen by camera with my laptop screen. I know the vector equation, I have camera calibrated.

However, I now need to know the equation of plane in which the screen lies. For this, I need camera coordinates of any 3 points on the screen.

Since camera is in the same plane as the screen, it can't "see" the screen, how do I estimate the top left corner of screen if I know that it is 17.5 cm to the left of the camera?

Is there a way to convert physical distance into camera coordinates?

I'm assuming in camera coordinates, the camera centre itself is (0,0,0) and therefore the left screen corner would be (-17.5cm,-1cm,0) - Z remaining 0 since its in same plane, & X,Y values being negative since its below to the left of camera. But how to get this in camera coordinates?