To find a x (-b), we first need to determine the vector -b and then compute the cross product.

To find $-\vec{b}$, we multiply each component of $\vec{b}$ by $-1$:

$$-\vec{b} = -(-\hat{i} + 3\hat{j} + \hat{k})$$ $$-\vec{b} = \hat{i} - 3\hat{j} - \hat{k}$$

We use the determinant formula for the cross product:

$$\vec{a} \times (-\vec{b}) = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & 0 \\ 1 & -3 & -1 \end{vmatrix}$$

Expand the determinant:

$$= \hat{i}((1)(-1) - (0)(-3)) - \hat{j}((2)(-1) - (0)(1)) + \hat{k}((2)(-3) - (1)(1))$$ $$= \hat{i}(-1 - 0) - \hat{j}(-2 - 0) + \hat{k}(-6 - 1)$$ $$= -1\hat{i} - (-2)\hat{j} + (-7)\hat{k}$$ $$= -\hat{i} + 2\hat{j} - 7\hat{k}$$

The calculated result is $-\hat{i} + 2\hat{j} - 7\hat{k}$.
Let's check the options:

(a) $-5\hat{i} + 10\hat{j} - 3\hat{k}$

(b) $\hat{i} + 2\hat{j} - 7\hat{k}$

(c) $5\hat{j} - 10\hat{j} + 3\hat{k} = -5\hat{j} + 3\hat{k}$

(d) None

Our calculated vector $-\hat{i} + 2\hat{j} - 7\hat{k}$ does not exactly match option (b) because of the sign of the $\hat{i}$ component. Since it does not match any of the options (a), (b), or (c), the correct choice is (d).

The final answer is $\boxed{\text{(d)}}$.