Question

If P,Q represent two points in affine space, we know that P-Q gives a vector but what is wrong in calculating P+Q

Answer 1

The vector resulting from subtraction P-Q does not depend on the specific coordinate system.
On the other hand, geometric interpretation of the result of adding P+Q depends on the coordinate system, e.g.,
* if P is at the origin, then P+Q=Q
* if Q is at the origin then P+Q=P
* if the origin is M, the midpoint of the segment PQ, then P+Q=M

Answer 2

Thanks :)