This simulation calculates the dot product for any two (2-D) vectors. Drag the head of each vector to change it. The numerical value of the dot product and a geometrical interpretation are drawn. The drop down list changes the order that the vectors are "dotted" with one another. Each space on the grid is one unit.

When is the dot product zero?

When is the dot product negative?

Given A and B, how could you use the dot product to calculate the angle between them?

There's another formula for calculating dot products (A_{x}B_{x} + A_{y}B_{y}). Why does it work?