The dot product obeys the usual foiling rule for multiplying out. In addition, the dot product is commutative. Those two facts should enable you to tell me the answer to your question.
Suppose that is the diameter of a circle with center , and that is a point on one of the two arcs joining and . Show that and are orthogonal. is from to . is from to . is from to .
I know if their dot product is zero, they are orthogonal. If the dot product is it would have to be zero because their magnitudes are the same.
Is this enough proof? I think it is.