return a common vector from others

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[The common starting point & transformation vector between Aa & Bb would be (3,3)1,2I have a point A with coordinates (a, b, c) and I am transforming it by vector [d, e, f].

I also have point B with coordinates (g, h, i) which will have a transformation vector of [j, k, l]

I need to find a starting point & transformation vector which is common to both.

Please, even if you cannot give me the actual answer, any pointers in the right direction would be good!