Which of the following is not equal to $w \cdot(u \times v)$ ?

If $[\bar{a} \bar{b} \bar{c}]=3$,then the volume of the parallelepiped with $2 \bar{a}+\bar{b}, 2 \bar{b}+\bar{c}, 2 \bar{c}+\bar{a}$ as coterminus edges is

If the origin $O(0,0,0)$ and the points $P(2,3,4)$,$Q(1,2,3)$,and $R(x, y, z)$ are co-planar,then:

Let $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$. If $\vec{c}$ is a vector such that $\vec{a} \cdot \vec{c}=11$,$\vec{b} \cdot(\vec{a} \times \vec{c})=27$ and $\vec{b} \cdot \vec{c}=-\sqrt{3}|\vec{b}|$,then $|\vec{a} \times \vec{c}|^2$ is equal to

If vectors $\vec{A} = 2i + 3j + 4k$,$\vec{B} = i + j + 5k$,and $\vec{C}$ form a left-handed system,then $\vec{C}$ is

If $x \cdot a = 0, x \cdot b = 0$ and $x \cdot c = 0$ for some non-zero vector $x$,then the true statement is