Hi Please help me with these questions, I really really don't know how to do them!

1.) Find the equation of the plane perpendicular to the line connecting A(1,4,2) and B(4,1,-4) and containing P such that AP:PB = 1:2

I got the vector AB which is 3i-3j-6k, then I subbed coordinates of point A into i, j and k and I got x-y-2z = -7, however the answer was x-y-2z = -1!

2.) Simplify AX-BX+BZ+YD-YZ-YD

I don't quite get what I am supposed to do..

3a.) Prove that vectors XY+YO+OZ+ZX = 0

I know that the resultant vector will be XX, will that be equal to 0? I'm confused though, why, how does XX look like?

All I know is that a x a = 0 in space.

3b.) If Vectors AO + OB = Vectors BO + OC then A, B, C are collinear.

I know to prove that points are collinear through component forms of the vectors.. am I supposed to make up component vectors here?

4.) Find the equation of the plane containing A(3,2,1) and the line x=1+t, y=2-t, z=3+2t

I know the vector/ direction vector is i-j+2k from the parametric equations.

I know that I have two position vectors, 3i+2j+k and i+2j+3k.

But then how do I continue?

Thank you very much I really appreciate this,

Thank you!