What's the necessary condition for that any three vectors are parallel to the edges of a triangle in the plane?

Question

• What's the necessary condition for that any three vectors are parallel to the edges of a triangle in the plane?

I answered the following:

The necessary condition is that the vectors are non-parallel.

Proof: To build a triangle, take three points in the plane such that not all three are collinear. Let $AB,AC$ line segments. Here we have that $AB\not\parallel AC$ because $A,B,C$ are not all three colinear. $BC\not\parallel BA$ and $CA\not\parallel CB$ for the same reason.

Is it correct?

Answer 1

$AB∦AC $ would be sufficient, you don't need all three statements.

Alternatively, $\overrightarrow{AB}\times\overrightarrow{AC}\neq0$, or any such permutation