# Vector algebra

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!

## Answers and Replies

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Galileo
Science Advisor
Homework Helper
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

Galileo
Science Advisor
Homework Helper
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.