We are given a non-zero vector $\vec A$ with constant magnitude $|\vec A| \neq 0$.

Check each option:

Option A: $\vec A \cdot \vec A = 0$

But, $\vec A \cdot \vec A = |\vec A|^2$ Since $|\vec A| \neq 0$, $|\vec A|^2 > 0$ So option A is false.

Option B: $\vec A \times \vec A < 0$

The cross product of any vector with itself is $\vec A \times \vec A = |\vec A||\vec A|\sin 0\,\hat n = 0$ A cross product is a vector, so writing $<0$ is not meaningful here. In any case, it is not negative. So option B is false.

Option C: $\vec A \times \vec A = 0$

Using $\vec A \times \vec A = |\vec A|^2 \sin 0\,\hat n = 0$ Hence option C is true.

Option D: $\vec A \times \vec A > 0$

Again, $\vec A \times \vec A = 0$, not positive. Also cross product is a vector quantity, so $>0$ is not meaningful. Thus option D is false.

Therefore, the correct expression is $\boxed{\vec A \times \vec A = 0}$

Comparison with stored correct answer:

Stored correct answer: C

Derived answer: C

They match.