Space geometry

Find the distance between two parallel planes \(\alpha \) and \(\beta \). \[ \begin{aligned} \alpha& \colon x - 1.5y - 3z - 1 = 0,\\ \beta &\colon 2x - 3y - 6z + 3 = 0 \end{aligned}\]

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 \(EFG\).

Find the angle between two lines and round your answer to the nearest minute. \[ \begin{aligned}p\colon x& = 2 - t , & \\y & = 3t , \\z & = 1 ;\ t\in \mathbb{R} \\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = 2s, & \\y & = 4s , \\z & = 1 - s;\ s\in \mathbb{R} \\ \end{aligned} \]