Are 3 Vectors Coplanar? Checking the Triple Product

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Homework Help Overview

The discussion revolves around determining the coplanarity of three vectors given by their coordinates. The original poster is attempting to use the triple product and the determinant of a matrix formed by these vectors to assess their relationship in space.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster calculates the determinant and finds it non-zero, leading to confusion regarding the coplanarity claim in the answer key. Other participants question the accuracy of the problem statement and the interpretation of coplanarity.

Discussion Status

Participants are exploring different interpretations of the vectors' relationships. Some assert that the vectors are coplanar, while others point out that the determinant indicates linear independence, suggesting they do not lie in the same plane. There is no explicit consensus on the matter, and various perspectives are being considered.

Contextual Notes

There is uncertainty regarding the correctness of the problem statement and the definitions being applied, particularly concerning the meaning of coplanarity and the implications of the determinant value.

teclo
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so, I'm trying to determine if the vectors
2,1,-1
1,1,0
2,-1,3

are coplanar. i take the triple product, finding the determinant of the matrix. it seems to be non-zero, but the answer key insists these are coplanar. am i wrong, or perhaps the book? any input would be appreciated!
 
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You're right. Did you copy the problem correctly?
 
did you check the vectors out themselves?...? they are coplanar.
 
coplanar means that they all exist on the same plane, right? i just made a vypthon program to draw all of the vectors as they are starting from the origin. it looks to me like the definitely span a parallelpiped, but i could certainly be wrong... now I'm even more confused
 
Well, the determinant is 6, so the three vectors are linearly independent. Since two of the vectors span a plane and the third is not a linear combination of the former two it does not lie in the same plane.
 

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