This tiny application demonstrates visually the results of the two-dimensional dot product and cross / perp dot product.
The products are calculated by two vectors that are given by the three red points. Vector v_{1} is defined as the vector that starts from point 1 and ends at point 2. Vector v_{2} is defined as the vector that starts from point 1 and ends at point 3.
Note that the red points can be moved by clicking and dragging them - the results of the products are instantly updated.

Notes about the Dot Product

The dot product of vectors v_{1} and v_{2} is defined as v_{1}.x * v_{2}.x + v_{1}.y * v_{2}.y .

If the two vectors are orthogonal, then the dot product is zero.

If two vectors face the same direction, the dot product is the product of the length of the vectors.

The dot product can also be defined as v_{1}.x * v_{2}.x + v_{1}.y * v_{2}.y = len(v_{1}) * len(v_{2}) * cos α where α is the angle between the two vectors.

The cross product of vectors v_{1} and v_{2} is defined as v_{1}.x * v_{2}.y - v_{1}.y * v_{2}.x .
Actually the cross product is not defined for two-dimensional vector - here it is better known as the perp dot product.

If the two vectors are orthogonal, then the dot product is equal to the area of the rectangle that both vectors form.

If two vectors face the same direction, the cross product is zero.

In general, the cross product is equal to the area of the parallelogram that both vectors form.

The cross product can also be defined as v_{1}.x * v_{2}.y - v_{1}.y * v_{2}.x = len(v_{1}) * len(v_{2}) * sin α where α is the angle between the two vectors.