Questions in vectors-m

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	In a triangle ABC, if $2\overrightarrow{AC}=3\overrightarrow{CB},$ then $2\overrightarrow{OA}+3\overrightarrow{OB}$ equals
	If $\overrightarrow{AO}+\overrightarrow{OB}=\overrightarrow{BO}+\overrightarrow{OC},$ then A, B, C form
	The sum of the three vectors determined by the medians of a triangle directed from the vertices is
	The position vector of the points which divides internally in the ratio 2 : 3 the join of the points $2\mathbf{a}-3\mathbf{b}$ and $3\mathbf{a}-2\mathbf{b},$ is
	If position vector of points A, B, C are respectively $\mathbf{i}, \mathbf{j}, \mathbf{k}$ . and $AB=CX,$ then position vector of point X is
	If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is
	If $A,\,B,\,C$ are the vertices of a triangle whose position vectors are a, b, c and G is the centroid of the $\Delta ABC,$ then $\overrightarrow{GA}+\overrightarrow{GB}\,+\overrightarrow{GC}$ is
	If $O$ is origin and $C$ is the mid point of $A(2,\,\,-1)$ and $B(-4,\,3)$ . Then value of $\overrightarrow{OC}$ is
	If $ABCDEF$ is regular hexagon, then $\overrightarrow{AD}\,+\overrightarrow{EB}+\overrightarrow{FC}=$
	If position vectors of a point A is $\vec{a} + 2\vec{b}$ and $\vec{a}$ divides AB in the ratio $2:3$ , then the position vector of B is