Finding Coplanar Vectors: r1v & r2v

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SUMMARY

The discussion focuses on determining the coplanarity of two vectors, r1v and r2v, defined in three-dimensional space using their components. The user highlights that if the vectors are perpendicular, the cross product (r1v cross r2v) equals zero, indicating they are coplanar. Additionally, it is established that two vectors are inherently coplanar if they do not coincide, while the concept of coplanarity is more relevant when considering three vectors.

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  • Understanding of vector representation in three-dimensional space
  • Knowledge of vector operations, specifically cross products
  • Familiarity with the concept of coplanarity in geometry
  • Basic proficiency in mathematical notation and operations
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  • Study the conditions under which three vectors are coplanar
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Philosophaie
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I have two vectors:

r1v=r1x*i + r1y*j + r1z*k
r2v=r2x*i + r2y*j + r2z*k

and

r1=Math.sqrt(r1x^2 + r1y^2 + r1z^2)
r2=Math.sqrt(r2x^2 + r2y^2 + r2z^2)

How do I find out if they are coplanar or not?

I know if they are perpendicular:

r1v cross r2v = 0
 
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You can use the next criterion:
http://mathworld.wolfram.com/Coplanar.html

Though I am not sure how you can find from your vectors the 4 points.

But obviously if the vectors don't coincide (i.e are actually the same vector) then they make up a plane, i.e coplanar.
 
Yeah, it's not really meaningful to ask if two vectors are or are not coplanar. You can ask if three vectors are coplanar, however.
 

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