Unit 13.2 Worked Example 5

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The planes \({{\text{p}}_{1}}\) and \({{\text{p}}_{2}}\) have equations \(\mathbf{r}\cdot \left( \begin{matrix}1 \\ -3 \\ 2 \\\end{matrix} \right)=-5\) and \(\mathbf{r}\cdot \left( \begin{matrix} 2 \\-1 \\ 3 \\\end{matrix} \right)=1\) respectively, and meet in the line \({{l}_{4}}\). Find

(i)

the vector equation for \({{l}_{4}}\),

(ii)

Find the acute angle between \({{\text{p}}_{1}}\) and \({{\text{p}}_{2}}\).