Consider the expression
$$ A^T V A=0 $$
where $V$ is a $l\times l$ strictly negative definite matrix and $A$ is a $l\times 1$ vector.
Is it correct to say
(1) $A^T V A=0$ if and only if $A=0_l$, where $0_l$ is a $l\times 1$ vector of zeros
or
(2) $A^T V A=0$ if and only if $||A||=0$, where $||\cdot ||$ is the norm
?