If $[\bar{a} \quad \bar{b} \quad \bar{c}]=4$,then the volume of the parallelepiped with coterminous edges $\bar{a}+2 \bar{b}$,$\bar{b}+2 \bar{c}$,and $\bar{c}+2 \bar{a}$ is:

Match the statements/expressions given in Column $I$ with the values given in Column $II$.

Column $I$	Column $II$
$(A)$ Root$(s)$ of the equation $2 \sin ^2 \theta + \sin ^2 2 \theta = 2$	$(p)$ $\frac{\pi}{6}$
$(B)$ Points of discontinuity of the function $f(x) = [\frac{6x}{\pi}] \cos [\frac{3x}{\pi}]$,where $[y]$ denotes the largest integer less than or equal to $y$	$(q)$ $\frac{\pi}{4}$
$(C)$ Volume of the parallelepiped with its edges represented by the vectors $\hat{i}+\hat{j}, \hat{i}+2\hat{j}$ and $\hat{i}+\hat{j}+\pi\hat{k}$	$(r)$ $\frac{\pi}{3}$
$(D)$ Angle between vectors $\vec{a}$ and $\vec{b}$ where $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors satisfying $\vec{a}+\vec{b}+\sqrt{3}\vec{c}=\overrightarrow{0}$	$(s)$ $\frac{\pi}{2}$
	$(t)$ $\pi$

If $a=2u+3v+7w$, $b=u+v-2w$ and $c=-u-2v-3w$, then $\left|\frac{[u, v, w]}{[a, b, c]}\right|(a+b+c) = $

Let $\vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+2 \hat{k}$. Let $\vec{d}$ be a vector which is perpendicular to both $\vec{a}$ and $\vec{b}$,and $\vec{c} \cdot \vec{d}=12$. Then $(-\hat{i}+\hat{j}-\hat{k}) \cdot(\vec{c} \times \vec{d})$ is equal to $........$.

If the vectors $2 \bar{i} + 4 \bar{j} - 3 \bar{k}$,$-\bar{i} + 2 \bar{j} + 3 \bar{k}$,and $p \bar{i} - 2 \bar{j} + \bar{k}$ are coplanar,then the unit vector in the direction of the vector $9p \bar{i} - 4 \bar{j} + 4 \bar{k}$ is

Let $OA, OB, OC$ be the co-terminal edges of a rectangular parallelopiped of volume $V$ and let $P$ be the vertex opposite to $O$. Then, $[\overrightarrow{AP} \overrightarrow{BP} \overrightarrow{CP}]$ is equal to