Question
Write the position vector of the point which divides the join of points with position vectors $3\overrightarrow{\text{a}} - 2\overrightarrow{\text{b}} \text{and } 2\overrightarrow{\text{a}} + 3\overrightarrow{\text{b}}$ in the ratio $2:1.$
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$ \begin{pmatrix} \text{3x + y}&\text{-y} \\ \text{2y - x}&\text{3} \\ \end{pmatrix}= \begin{pmatrix} \text{1}&\text{2} \\ \text{-5}&\text{3} \\ \end{pmatrix}.$