Find the plane containing the two lines $x = 3+t,y=-2t,z=4+2t$ and $x = 3-t, y = 3t, z = 4+4t$.

Given two lines, what properties do the lines need to have to find a plain containing them both?

Determine if the following lines are parallel, skew, or intersecting.

Find the line where the two planes intersect: $x + y + z = 3$ and $x-3y-z = 0$. What is the angle of intersection?

When do two planes intersect?

Write down a line going through the point $(1,2,3)$ and perpendicular to the plane $x+y+z = 4$. What is the distance from $(1,2,3)$ to the plane?