Calculate with three-dimensional vectors and test independence
Use an orthonormal Cartesian basis i,j,k
Find c=m a+n b from the stated coefficients
\[\mathbf a=\begin{pmatrix}2\\-1\\-2\end{pmatrix},\qquad\mathbf b=\begin{pmatrix}2\\2\\-1\end{pmatrix}\]
\[m=1,\quad n=2\]