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Well, whenver you do dot product you are always given two sets of coordinate. In order to have them starting at different location you'd need (at least) 3 sets of coordinates, which I you can't do dot product w/. Hence the convention that we assume all vectors start from origin (for most of the problems)
thedot product of two vectors is a quantity with the value = product of 2 vectors' lengths and cos(angle). so, think of it, when you have two vectors creating a different angle than the one in your picture, just change the value of the angle in the cos(angle). so yes, you can use it as long as you know the value of the angle and the lengths of the vectors
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