If the sum of three vectors in R3 is zero, must they lie in the same plane?

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- Feb 17th 2013, 02:02 PMCivy71Sum of 3 vectors in R3
If the sum of three vectors in R3 is zero, must they lie in the same plane?

- Feb 17th 2013, 07:53 PMchiroRe: Sum of 3 vectors in R3
Hey Civy71.

They could lie all on the same line or the same plane. They all lie on the same point if all vectors are the zero vector. - Feb 17th 2013, 07:55 PMMacstersUndeadRe: Sum of 3 vectors in R3
Let the three vectors be

If the sum of the three vectors is the zero vector, then these vectors are linearly dependent since so must lie on the same plane spanned by and . Hence all three vectors lie on the same plane - Feb 18th 2013, 06:45 AMCivy71Re: Sum of 3 vectors in R3
Thanks for the help MacstersUndead. Cool Avatar picture.