Mathematics

Problem

Prove that for any vectors

\mathbf{a},\mathbf{b},\mathbf{c}\in\mathbb{R}^3

, the scalar product is distributive over addition, i.e.,

\mathbf{a}\cdot(\mathbf{b}+\mathbf{c})=\mathbf{a}\cdot\mathbf{b}+\mathbf{a}\cdot\mathbf{c}