# Given vectors OA and OB calculate vector AB

So the teacher said it's like this OB - OA = AB and I don't understand it. Why aren't we doing this instead: OA - OB? aren't they the same thing?

• Order matters, since vectors have a direction. Convince yourself that $\vec {OA}+\vec {AB}=\vec {OB}$ which is equivalent to what the teacher said.
– lulu
Jan 18, 2019 at 17:04

Draw a diagram, labeling three points O, A, and B, and draw the vectors between them. In particular, remember that the vector OA goes from O to A, and remember that -OA is from A to O. Then draw out OB - OA, and OA - OB and observe whether they're the same thing or not.

Ask Tom and Jerry to go from O to B. Tell them that the start point is the tail and the end point is the head of the vector or arrow.

Tom goes directly to B and Jerry detours via point A before heading to B. Whether OB or OA+AB their effective effective displacement has remained the same.