Question

How do I calculate the dot product of two vectors?

Answer 1

To calculate the dot product (Euclidean inner product) multiply corresponding components and add the resulting products. If $\mathbf{u}=\left(u_{1}, u_{2}, \ldots, u_{n}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}, \ldots, v_{n}\right)$ are vectors in $R^{n}$, then the dot product (also called the Euclidean inner product) of $\mathbf{u}$ and $\mathbf{v}$ is denoted by $\mathbf{u} \cdot \mathbf{v}$ and is defined by $$ \mathbf{u} \cdot \mathbf{v}=u_{1} v_{1}+u_{2} v_{2}+\cdots+u_{n} v_{n} $$