How to calculate the fourth vertex of a parallelogram

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SUMMARY

The discussion focuses on calculating the fourth vertex of a parallelogram given three vectors: A=(1,3,4), B=(2,5,3), and C=(1,0,0). The user seeks assistance in determining the unknown vertex D=(x,y,z) by applying the properties of parallelograms, specifically that AB=CD and AC=BD. The conversation emphasizes the importance of vector subtraction, where AB is calculated as B - A.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with the properties of parallelograms
  • Basic knowledge of vector operations, specifically vector subtraction
  • Ability to manipulate coordinates in three-dimensional space
NEXT STEPS
  • Study vector subtraction in detail to understand how to calculate differences between vectors
  • Explore the properties of parallelograms, focusing on vector relationships
  • Learn about coordinate geometry in three dimensions
  • Practice problems involving the calculation of unknown vertices in geometric shapes
USEFUL FOR

Students of geometry, mathematicians, and anyone interested in vector mathematics and geometric properties will benefit from this discussion.

mercuryman
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given 3 vectors : a=(1,3,4) b=(2,5,3) c=(1,0,0)
 
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welcome to pf!

hi mercuryman! welcome to pf! :wink:
mercuryman said:
given 3 vectors : a=(1,3,4) b=(2,5,3) c=(1,0,0)

tell us what you think :smile:
 
hi mercuryman! :wink:
mercuryman said:
Hi
I've marked the unknown vertex d=(x,y,z)
and tried to calculate its values by the fact that AB=CD and AC=BD and I'm missing something.. can u help?

do you know what vectors are?

if so, use AB = B - A etc :smile:
 

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