Question

What happens when I multiply a vector by itself?

Answer 1

There are two kinds of products with vectors, the scalar product and the vector product.

Let us have a vector A.
Then A. A = `A^2`, where `A` is the magnitude of A.

In the case of a cross product,
A `X` A = `0`, since, the angle the vector makes with itself is `0` and `Sin 0 = 0`.