I don't undertand what you are saying here. You were asked for an equation of the plane, pi. This is the parametric equations for a line, not a plane.
b.) The plane containing the points A,B, C is denoted by pi and the line passing through D perpendicular to pi is denoted by L. The point of intersection of L and pi is denoted by P.
bi.) FInd the cartesian equation of pi.
AB is the direction vector of pi, I thought. And then I'll need a point so
I got x=1, y=3-t, z=1+3t
Yes, this is correct.
bii.) FInd the cartesian equation of L.
The result of the cross product in ai.) is the direction vector of L, I thought. Dotting it by the direction vector of pi, I will get a zero.
So my answer was
x=5-5t, y=-2+3t, z=1+t