Let the lines $r \equiv \left\{ \begin{array} { l } x + y + 2 = 0 \\ y - 2 z + 1 = 0 \end{array} \right.$ and $s \equiv \left\{ \begin{array} { l } x = 2 - 2 t \\ y = 5 + 2 t \\ z = t \end{array} , t \in \mathbb { R } \right.$. a) (1.5 points) Study the relative position of the given lines and calculate the distance between them. b) ( 0.5 points) Determine an equation of the plane $\pi$ that contains the lines $r$ and $s$. c) (0.5 points) Let P and Q be the points on the lines $r$ and $s$, respectively, that are contained in the plane with equation $z = 0$. Calculate an equation of the line passing through points $P$ and $Q$.
Let the lines $r \equiv \left\{ \begin{array} { l } x + y + 2 = 0 \\ y - 2 z + 1 = 0 \end{array} \right.$ and $s \equiv \left\{ \begin{array} { l } x = 2 - 2 t \\ y = 5 + 2 t \\ z = t \end{array} , t \in \mathbb { R } \right.$.\\
a) (1.5 points) Study the relative position of the given lines and calculate the distance between them.\\
b) ( 0.5 points) Determine an equation of the plane $\pi$ that contains the lines $r$ and $s$.\\
c) (0.5 points) Let P and Q be the points on the lines $r$ and $s$, respectively, that are contained in the plane with equation $z = 0$. Calculate an equation of the line passing through points $P$ and $Q$.