Vectors and Points 2

Coordinates of vectors roaming around the plane

Suppose V is a vector with its tail at point a and its head at b, and V₀ is the same vector when its tail is at the origin. What is the relation between the coordinates of V and those of V₀?

Try moving points a, b, and vector V, and see how the coordinates change.

Use Tabulate to make a list of the coordinates at various positions. See if you can figure out the rule.

The rule: If p₀ is the head of V₀ then the coordinates of p₀ are the differences of the coordinates of b and a. Check it out!