Q1: Consider a $3$-dimensional volume function $\mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w})$. Which operation is correct?

A1: $$\mathrm{vol}_3(\mathbf{u}, 2\mathbf{v}, \mathbf{w}) = 2 \cdot \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

A2: $$\mathrm{vol}_3(\mathbf{u}, \mathbf{v} + \mathbf{u}, \mathbf{w}) = 2 \cdot \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

A3: $$\mathrm{vol}_3(2 \mathbf{u}, 2 \mathbf{v}, 2 \mathbf{w}) = 2 \cdot \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

A4: $$\mathrm{vol}_3(2 \mathbf{u}, 2 \mathbf{v}, 2 \mathbf{w}) = 4 \cdot \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

Q2: Consider a $3$-dimensional volume function $\mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w})$. Which operation is correct?

A1: $$\mathrm{vol}_3(\mathbf{u}, \mathbf{v} + \mathbf{u} +\mathbf{w}, \mathbf{w}) = \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

A2: $$\mathrm{vol}_3(\mathbf{u}, \mathbf{v} + \mathbf{u}, \mathbf{w}) = 2 \cdot \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

A3: $$\mathrm{vol}_3(2 \mathbf{u}, \mathbf{v}, 2 \mathbf{w}) = \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

A4: $$\mathrm{vol}_3(2 \mathbf{u}, 2 \mathbf{v}, 2 \mathbf{w}) = 4 \cdot \mathrm{vol}_3(\mathbf{u}, \mathbf{v}, \mathbf{w}) $$

Q3: Consider the two-dimensional volume form $\mathrm{vol}_2(\mathbf{u}, \mathbf{v})$. What is the correct formula to calculate it?

A1: $\mathrm{vol}_2(\mathbf{u}, \mathbf{v}) = u_1 v_2 - v_1 u_2$

A2: $\mathrm{vol}_2(\mathbf{u}, \mathbf{v}) = u_2 v_2 - v_1 u_1$

A3: $\mathrm{vol}_2(\mathbf{u}, \mathbf{v}) = u_1 v_1 - v_2 u_2$

A4: $\mathrm{vol}_2(\mathbf{u}, \mathbf{v}) = u_2 v_1 - v_2 u_1$