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

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SUMMARY

To find the fourth coordinate of a parallelogram in 3D space when given three vertices, utilize vector addition. Specifically, if you have three vertices A, B, and C, the fourth vertex D can be calculated using the formula D = A + (C - B). This approach leverages the property that opposite sides of a parallelogram are equal in magnitude and direction. Understanding vector operations is crucial for accurately determining the coordinates of the fourth vertex.

PREREQUISITES
  • Understanding of 3D coordinate systems
  • Familiarity with vector addition and subtraction
  • Knowledge of geometric properties of parallelograms
  • Basic skills in linear algebra
NEXT STEPS
  • Study vector operations in 3D space
  • Learn about the properties of parallelograms and parallelepipeds
  • Explore applications of vectors in computer graphics
  • Investigate geometric transformations in three dimensions
USEFUL FOR

Mathematicians, computer graphics developers, and anyone involved in 3D modeling or geometric computations will benefit from this discussion.

yourmom98
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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
 
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Could you use the fact that opposite sides of a parallelogram are parallel and equal in magnitude (basically, the same vector)?
 
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.
 
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.
 

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