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Illustration Orthonormal basis vectors - Cartesian coordinate system

Orthonormal basis vectors - Cartesian coordinate system
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.