How do I show vector multiplication graphically?

Well! after reading this answer people will realize that I am the most suitable guy for answering this question There are two ways to multiply two vectors together. read more

Since we do not have the ability to arbitrarily scale vectors at this time, we can't really demonstrate these properties of the dot product graphically. We will be able to easily demonstrate these later. The other way to multiply two vectors is called the cross-product. The cross-product is denoted with an ×. read more

The vector changes in length, while its direction remains the same. If the vector's magnitude was previously | v|, once it is multiplied by a scalar we have | av| = a| v|. Note that if | a| > 1 the new vector will be longer. read more

Since the projection of a vector on to itself leaves its magnitude unchanged, the dot product of any vector with itself is the square of that vector's magnitude. A · A = AA cos 0° = A 2. Applying this corollary to the unit vectors means that the dot product of any unit vector with itself is one. read more