How Can I Find the 4th Coordinate of a Parallelogram in 3D Space?

[yourmom98]

i am given the (x,y,z) coordinates of 3 sides of a parallelogram how do i go about finding the 4 coordinate. do i find the distance between points using the same way to find vectors then try to find direction angles or something like that? because there is no slope or anything to compare too. Also any tips about geometry in 3 space would be greatly appreciated

 

[SpiffyKavu]

Could you use the fact that opposite sides of a parallelogram are parallel and equal in magnitude (basically, the same vector)?

 

[HallsofIvy]

You mean, I presume, a parallelpiped, the 3 dimensional analog of a parallelogram. If you are given three vertices, then you know three vectors that form the sides of the parallelpiped. Adding the three vectors to one vertex will give you the opposite vertex.

 

[yourmom98]

Thanks HallsofIvy for correcting me. But i don't understand if I am given 3 vertices i would only know 2 vectors that form the parallelepiped and one vector that is a diagonal of the parallelepiped.