X.B.1.1 Vectors in a Cartesian coordinate system

A vectorial force $f$ can be expressed by its components $\left\{f_1,f_2,f_3\right\}$ in the Cartesian coordinate system $\left\{O,e_1,e_2,e_3\right\}$ characterized by its origin $O$ and its three unit length mutually orthogonal vectors $e_1$, $e_2$ and $e_3$. Then the vector $f$ corresponds to:

In the rest of the text the components of a vector $f$ are denoted $f_i$ and one uses the Bose-Einstein convention of summation on repeated indices so that the previous expression is simply written: