## Level 2

**Level 2**requires school mathematics. Suitable for pupils.

# Illustration **Orthonormal basis vectors - Cartesian coordinate system**

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Three-dimensional Cartesian (orthogonal) coordinate system spanned by the following three basis vectors:

`\[ \boldsymbol{\hat{e}}_x ~=~ \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}, ~~\boldsymbol{\hat{e}}_y ~=~ \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}, ~~\boldsymbol{\hat{e}}_z ~=~ \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \]`The three basis vectors are orthonormal, i.e. *orthogonal* to each other and *normalized*.