Question

What is the dot product of a vector with itself?

Answer 1

1. A vector's dot product with itself is the square of its magnitude.
2. For example, let $A$ be a vector then the dot product of this vector with itself is $A.A=AA\cos 0=A^2\left(1\right)=A^2$where $\cos 0$ is the angle of this vector with itself.
3. The dot product of two vectors is commutative, which means that the order of the vectors in the product is irrelevant.
4. When a vector is multiplied by a constant, its dot product with any other vector is multiplied by the same constant.