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What are the necessary and sufficient conditions in high school math problems?
You should have understood the necessary conditions.

Just say why is not a sufficient condition.

If the three vectors a, b and c are parallel,

A and B are in the same direction, but C is in the opposite direction. The length of A plus the length of B is equal to the length of C. ..

Then the condition of a vector +b vector +c vector =0 vector is also satisfied.

But these three vectors can't form a triangle.

So it's not enough.