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Mathematics · Glossary

What is Sum of two vectors?

Also known as: vector sum

Definition 6.4 High School Mathematics · Chapter 6 — Vectors

The sum u⃗+v⃗\vec u + \vec v is the displacement obtained by performing u⃗\vec u then v⃗\vec v.

Two pictures of the sum: tip-to-tail (Chasles’ relation, left) and the parallelogram rule (right). Two pictures of the sum: tip-to-tail (Chasles’ relation, left) and the parallelogram rule (right).
Two pictures of the sum: tip-to-tail (Chasles’ relation, left) and the parallelogram rule (right).

Examples

Example 6.7 (Simplifying with Chasles)

Simplify MN→+NP→+PQ→\vect{MN} + \vect{NP} + \vect{PQ}: chaining the displacements gives MQ→\vect{MQ}. Simplify AB→−AC→\vect{AB} - \vect{AC}: rewrite the difference as a sum with the opposite vector,

AB→−AC→=AB→+CA→=CA→+AB→=CB→.\vect{AB} - \vect{AC} = \vect{AB} + \vect{CA} = \vect{CA} + \vect{AB} = \vect{CB}.
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