NOTE: I know almost nothing about vectors:
BUT
Here is a youtube for getting the equation of the plane that passes through 3 specific points
https://www.youtube.com/watch?v=uvR2q2LQxNc
And here is one to help you find the angle between two vectors (you need an angle of 90 degrees.
https://www.youtube.com/watch?v=QWIZXRjMspI
I muddled through these and possibly came up with an answer but I expect you are capable of doing it just as easily as me.
Try doing the video examples then try doing your own one.