Finding Coplanar Vectors: r1v & r2v

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In summary, the conversation discusses two vectors, r1v and r2v, and how to determine if they are coplanar or not. It suggests using the fact that if the vectors are perpendicular, their cross product will be equal to 0. It also mentions the criterion for coplanarity and the need for four points to determine if the vectors lie on a plane. However, it notes that it is not meaningful to ask if two vectors are coplanar, but rather three vectors.
  • #1
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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  • #2
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.
 
  • #3
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.
 

FAQ: Finding Coplanar Vectors: r1v & r2v

What are coplanar vectors?

Coplanar vectors are vectors that lie on the same plane. This means that they can be drawn in a two-dimensional space and do not require a third dimension to be represented.

How do I find coplanar vectors?

To find coplanar vectors, you can use the cross product or dot product method. The cross product method involves taking the cross product of two vectors to determine if they are parallel or perpendicular, while the dot product method involves taking the dot product of two vectors to determine if they are collinear or perpendicular.

What is the importance of finding coplanar vectors?

Finding coplanar vectors is important in various fields of science and engineering, such as physics, geometry, and computer graphics. It allows us to analyze and understand the relationship between different vectors and how they behave in a two-dimensional space.

Can coplanar vectors be non-parallel?

Yes, coplanar vectors can be non-parallel. As long as they lie on the same plane, they are considered coplanar, regardless of their direction or magnitude.

Are there any real-life applications of coplanar vectors?

Yes, coplanar vectors have various real-life applications, such as in navigation systems, flight simulations, and architectural design. They are also used in physics to analyze the motion of objects in a two-dimensional space.

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