Vectors in a Cartesian coordinate system

X.B.1.1 Vectors in a Cartesian coordinate system

A vectorial force $f$ can be expressed by its components ${f_{1}, f_{2}, f_{3}}$ in the Cartesian coordinate system ${O, e_{1}, e_{2}, e_{3}}$ 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:

f = \sum_{i = 1}^{3} f_{i} e_{i} .

In the rest of the text the components of a vector $f$ are denoted $f_{i}$ and the Einstein convention of summation on repeated indices is used, so that the previous expression is simply written:

f = f_{i} e_{i} .

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