Find the relationship and the acute angles between the two planes. If the planes are parallel to each other, find the perpendicular distance between the planes, otherwise, find the equation of line which two planes intersect.
${{\Pi }_{1}}:\mathbf{r}=\left( \begin{matrix} 1\\ 0\\ -3 \\\end{matrix} \right)+\lambda \left( \begin{matrix} -2 \\1\\ 0 \\\end{matrix} \right)+\mu \left( \begin{matrix} 1\\ -2\\ 3 \\\end{matrix} \right);\lambda ,\mu \in \mathbb{R}$, 
${{\Pi }_{2}}:(-1+2t-3s)\mathbf{i}+(-3-t+s)\mathbf{j}+(5+2t-s)\mathbf{k};s,t\in \mathbb{R}$

Find the relationship and the acute angles between the two planes. If the planes are parallel to each other, find the perpendicular distance between the planes, otherwise, find the equation of line which two planes intersect.

${{\Pi }_{1}}:\mathbf{r}=\left( \begin{matrix} 1\\ 0\\ -3 \\\end{matrix} \right)+\lambda \left( \begin{matrix} -2 \\1\\ 0 \\\end{matrix} \right)+\mu \left( \begin{matrix} 1\\ -2\\ 3 \\\end{matrix} \right);\lambda ,\mu \in \mathbb{R}$, 

${{\Pi }_{2}}:(-1+2t-3s)\mathbf{i}+(-3-t+s)\mathbf{j}+(5+2t-s)\mathbf{k};s,t\in \mathbb{R}$

Vectors - Relationships Between Two Planes

Question 017770cd

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