B

Find the distance between two parallel lines \(p\) and \(q\). \[ \begin{aligned}p\colon x& = 2, & \\y & = 3t, \\z & = 1 - t;\ t\in \mathbb{R} \\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = 3, & \\y & = 6s, \\z & = 1 - 2s;\ s\in \mathbb{R} \\ \end{aligned} \]

Find the distance between the point \(A = [-1;1;0]\) and the plane \(\alpha \). \[ \alpha \colon 12y + 5z - 2 = 0 \]

Find the distance between the line \(p\) and the plane \(\alpha \). \[ \alpha \colon x-3y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] p\colon x& = 1 + t, & \\y & = -3t, \\z & = 2;\ t\in \mathbb{R} \\ \end{aligned} \]

The points \(A = [0;5;0]\), \(B = [5;5;0]\), \(C = [5;0;0]\), \(D = [0;0;0]\) define a cube \(ABCDEFGH\). Find the distance between the line \(AB\) and the plane \(EFG\).