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.

[list=1][*]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[sub]x[/sub]B[sub]x[/sub] + A[sub]y[/sub]B[sub]y[/sub]). Why does it work?[/*][/list]