For three vectors $u, v, w$,which of the following expressions is not equal to any of the remaining three?

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors representing the coterminous edges of a parallelepiped of volume $4$ cubic units,then find the value of $(\vec{a} + \vec{b}) \cdot (\vec{b} \times \vec{c}) + (\vec{b} + \vec{c}) \cdot (\vec{c} \times \vec{a}) + (\vec{c} + \vec{a}) \cdot (\vec{a} \times \vec{b})$.

Let the vectors $\vec{u} = (2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k}$,$\vec{v} = (1+b) \hat{i}+2 b \hat{j}-b \hat{k}$,and $\vec{w} = (2+b) \hat{i}+2 b \hat{j}+(1-b) \hat{k}$ where $a, b, c \in \mathbb{R}$ be co-planar. Then which of the following is true?

If $[a, b, c] = 3$, then the volume (in cubic units) of the parallelepiped with $2a+b$, $2b+c$, and $2c+a$ as edges is:

If the vectors $\vec{a} + \lambda \vec{b} + 3\vec{c}$,$-2\vec{a} + 3\vec{b} - 4\vec{c}$,and $\vec{a} - 3\vec{b} + 5\vec{c}$ are coplanar,and $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar,find the value of $\lambda$.

If $u, v$ and $w$ are three non-coplanar vectors,then $(u + v - w) \cdot [(u - v) \times (v - w)]$ equals