Vectors - Distance from a Point to a Plane

Vectors - Distance from a Point to a Plane

\({{\Pi }_{1}}:\mathbf{r}=\left( \begin{matrix}1  \\3  \\1  \end{matrix} \right)+\lambda \left( \begin{matrix} 2  \\-2  \\ 1  \end{matrix} \right)+\mu \left( \begin{matrix}1  \\ 5  \\3  \end{matrix} \right);\lambda ,\mu \in \mathbb{R}\),

\({{\Pi }_{2}}:(2t+3s)\mathbf{i}+(1-2t+3s)\mathbf{j}+(-2+t+4s)\mathbf{k};s,t\in \mathbb{R}\)

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Answer:Parallel, \(0^\circ\), distance \(=\frac{15}{\sqrt{290}}\) units

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