Description

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 v₁ is defined as the vector that starts from point 1 and ends at point 2. Vector v₂ 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 v₁ and v₂ is defined as v₁.x * v₂.x + v₁.y * v₂.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 v₁.x * v₂.x + v₁.y * v₂.y = len(v₁) * len(v₂) * cos α where α is the angle between the two vectors.

For further information of the dot product, see also my article Derivation of the two-dimensional dot product.

Notes about the Cross / Perp dot Product

The cross product of vectors v₁ and v₂ is defined as v₁.x * v₂.y - v₁.y * v₂.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 v₁.x * v₂.y - v₁.y * v₂.x = len(v₁) * len(v₂) * sin α where α is the angle between the two vectors.

Hope you liked it!

Sunshine2k, August 2k17

History

2017/08/25: Initial release.