3 vectors ¯a,¯b,¯c can always form the sides of a triangle if ¯a+¯b+¯c=0
False
The given condition is valid only when the 3 vectors or are not collinear. For instance consider the situation in which ¯a=^i+^j+^k,b=2^i+2^j+2^k, c=−(3^i+3^j+3ˆk). In this case we can still have ¯a+¯b+¯c=0 but they lie along the vector ^i+^j+^k.
But in case when no 2 of the given vectors are parallel and the given condition is valid then we can say they do form sides of a triangle. Therefore the given statement is not always true.