\begin{definition}[Definition:Direction Cosine]
Let $\mathbf a$ be a vector quantity embedded in a Cartesian $3$-space.
Let the angles which $\mathbf a$ makes with the $x$-axis, $y$-axis and $z$-axis be $\alpha$, $\beta$ and $\gamma$ respectively.
Then the '''direction cosines''' of $\mathbf a$ are $\cos \alpha$, $\cos \beta$ and $\cos \gamma$, defined individually such that:
:$\cos \alpha$ is the '''direction cosine of $\mathbf a$ with respect to the $x$-axis'''
:$\cos \beta$ is the '''direction cosine of $\mathbf a$ with respect to the $y$-axis'''
:$\cos \gamma$ is the '''direction cosine of $\mathbf a$ with respect to the $z$-axis'''.
\end{definition}