If $A(2, 3, 5)$,$B(1, 2, 3)$,$C(-5, 4, -2)$,and $D(1, 10, 10)$,then ...

Statement $(A):$ In $\Delta ABC$,$\overline{AB} + \overline{BC} + \overline{CA} = 0$.
Reason $(R):$ If $\overline{AB} = \vec{a}$ and $\overline{BC} = \vec{b}$,then $\overline{AC} = \vec{a} + \vec{b}$ (Triangle Law of Addition).

If the collinear points $A, B$ and $C$ have position vectors respectively $(1, x, 3), (3, 4, 7)$ and $(y, -2, -5)$, then $x+y=$

In the triangle $ABC,$ if $\overrightarrow{AB} = a, \overrightarrow{AC} = c, \overrightarrow{BC} = b$,then which of the following is correct?

Let $O$ be the origin,$A$ and $B$ be two points with position vectors $-3 \hat{i}-3 \hat{j}+4 \hat{k}$ and $4 \hat{i}-4 \hat{j}-3 \hat{k}$ respectively. Let $P$ be a point such that the line drawn through $P$ parallel to $\overrightarrow{OB}$ meets $OA$ in $L$ and another line through $P$ parallel to $\overrightarrow{OA}$ meets $OB$ in $M$. If $L$ divides $OA$ in the ratio $2:3$ and $M$ divides $OB$ in the ratio $3:2$,then the distance from $O$ to $P$ is

Let $A, B, C, D$ be the points in the plane with position vectors $\vec{a} = -2\hat{i} - \hat{j}$, $\vec{b} = 4\hat{i}$, $\vec{c} = 3\hat{i} + 3\hat{j}$, and $\vec{d} = -3\hat{i} + 2\hat{j}$ respectively. Then $ABCD$ is: