If $P$ is the point of intersection of the diagonals of a parallelogram $ABCD$ and $O$ is any point,then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} + \overrightarrow{OD} = .......$

Let $\triangle PQR$ be a triangle. Let $\vec{a}=\overline{QR}, \vec{b}=\overline{RP}$ and $\vec{c}=\overline{PQ}$. If $|\vec{a}|=12, |\vec{b}|=4\sqrt{3}$ and $\vec{b} \cdot \vec{c}=24$,then which of the following is (are) true?
$(A) \frac{|\vec{c}|^2}{2}-|\vec{a}|=12$
$(B) \frac{|\vec{c}|^2}{2}+|\vec{a}|=30$
$(C) |\vec{a} \times \vec{b}+\vec{c} \times \vec{a}|=48\sqrt{3}$
$(D) \vec{a} \cdot \vec{b}=-72$

If $ABCD$ is a quadrilateral,then the resultant force represented by $\vec{BA}, \vec{BC}, \vec{CD}$ and $\vec{DA}$ is equal to:

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$,$\vec{b}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{d}=\vec{a} \times \vec{b}$. If $\vec{c}$ is a vector such that $\vec{a} \cdot \vec{c}=|\vec{c}|$,$|\vec{c}-2\vec{a}|^2=8$ and the angle between $\vec{d}$ and $\vec{c}$ is $\frac{\pi}{4}$,then $|10-3\vec{b} \cdot \vec{c}|+|\vec{d} \times \vec{c}|^2$ is equal to . . . . . .

If points $D, E, F$ divide the sides $BC, CA, AB$ of $\triangle ABC$ in the ratios $1:4, 3:2, 3:7$ respectively,and point $K$ divides $AB$ in some ratio,then $(\overrightarrow{AD} + \overrightarrow{BE} + \overrightarrow{CF}) : \overrightarrow{CK} = ......$

If $\vec{a}+l \vec{b}+l^2 \vec{c}=0$ and $\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}=3(\vec{b} \times \vec{c})$, then the minimum value of such $l$ is