This method is very similar to the third method for addition with components. Here is another technical observation with little motivation except for consequences that will follow. Scalar Multiplication and a First Distributive Law for it. Drawing parallelograms, tessellating the plane with them, implies or suggests that multiplication of vectors by whole numbers and then fractions distributes over the sum of two different vectors. Here is motivation if not a Euclidean proof, for the distributive of scalar multiplication over vector addition.
Rotation distributes over addition.
Here is a second distributive law. It follows from the assumption that a parallelogram is a rigid body. Polar Multiplication distributes over addition. All trademarks and copyrights on this page are owned by their respective owners. Copyright to comments contributions are owned by the Poster.