Vector components

Choose reference coordinates, express components, and distinguish position from displacement.

Meaning

Components describe changes along each coordinate-axis direction. The vector from A to B is B's coordinates minus A's.

Example

If A is and B is then The opposite vector reverses the signs.Adding the displacement to the starting point must reach the endpoint: A+displacement=B. Thus displacement=B−A; check (1,4)+(4,−2)=(5,2).Distinguish point coordinates from components between points. A position vector goes from the chosen origin to the point.

Practice for this concept

Scope and references

Topics

Position vectors, coordinate notation, plane and space vectors

Learning goal

Choose reference coordinates, express components, and distinguish position from displacement.

Helpful background

Connect coordinate axes with vector operations.