Given that \(\overrightarrow{PQ}=\begin{pmatrix}-3\\7\end{pmatrix}\) and \(4\overrightarrow{PR}=\begin{pmatrix}-2\\8\end{pmatrix}\), find \(\overrightarrow{RQ}\).[2]
The vectors \(\mathbf a\), \(\mathbf b\) and \(\mathbf c\) are such that \(\mathbf a=\alpha\mathbf i+6\mathbf j\), \(\mathbf b=4\mathbf i+\beta\mathbf j\) and \(\mathbf c=(2\alpha+5\beta)\mathbf i+20\mathbf j\), where \(\alpha\) and \(\beta\) are scalars.
Given that \(\mathbf c=3\mathbf a-2\mathbf b\), find the values of \(\alpha\) and \(\beta\).[3]
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