Thread: Vectors, planes

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!

Hey Tutu.

Can you show a bit more detail for how you figured these out? One at a time is OK if they end up being a bit long for one post.

Originally Posted by Tutu

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 , however the answer was x-y-2z = -1!

Actually, you did get the correct answer. I too would like to see some of your work. What value did you get for and how did you get it?

Thank you for your replies!

I don't think I'm right in my steps but here they are, they are very short because I basically fumbled my way through to get something..

1.) I got the vector AB which is 3i-3j-6k ( I took A x B ), 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!
I didn't get a value for P. I didn't know how to get it, moreover, is it important to get it?

2.)
3.)

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 had taken the direction vector from the coefficients of t ).
I know that I have two position vectors, 3i+2j+k(Point A) and i+2j+3k(From the parametic equations, where the position vectors are the ones that are not attached to t).
But then how do I continue?

Please help me and thank you!