Thread: Sum of 3 vectors in R3

1. Sum of 3 vectors in R3

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

2. Re: 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.

3. Re: Sum of 3 vectors in R3

Let the three vectors be $v_1,v_2,v_3$

If the sum of the three vectors is the zero vector, then these vectors are linearly dependent since $v_3 = -v_1 -v_2$ so $v_3$ must lie on the same plane spanned by $v_1$ and $v_2$. Hence all three vectors lie on the same plane

4. Re: Sum of 3 vectors in R3

Thanks for the help MacstersUndead. Cool Avatar picture.