Questions in vectors-m

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	If in the given figure $\overrightarrow{OA}=\mathbf{a},\,\,\,\overrightarrow{OB}=\mathbf{b}$ and $AP\,\,:\,\,PB=m\,\,:\,\,n,$ then $\overrightarrow{OP}=$
	If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then $\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}$ is
	If $\mathbf{a}$ and $\mathbf{b}$ are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that $\overrightarrow{AC}=3\overrightarrow{AB}$ is
	The position vectors of A and B are $\mathbf{i}-\mathbf{j}+2\mathbf{k}$ and $3\mathbf{i}-\mathbf{j}+3\mathbf{k}.$ The position vector of the middle point of the line AB is
	If ABCD is a parallelogram and the position vectors of A, B, C are $\mathbf{i}+3\mathbf{j}+5\mathbf{k},\,\,\mathbf{i}+\mathbf{j}+\mathbf{k}$ and $7\mathbf{i}+7\mathbf{j}+7\mathbf{k},$ then the position vector of D will be
	P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then $\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}=$
	If the position vectors of the point A, B, C be i, j, k respectively and P be a point such that $\overrightarrow{AB}=\overrightarrow{CP},$ then the position vector of P is
	If the position vectors of the points A, B, C, D be $2\mathbf{i}+3\mathbf{j}+5\mathbf{k},$ $\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,-5\mathbf{i}+4\mathbf{j}-2\mathbf{k}$ and $\mathbf{i}+10\mathbf{j}+10\mathbf{k}$ respectively, then
	If the position vector of one end of the line segment AB be $2\mathbf{i}+3\mathbf{j}-\mathbf{k}$ and the position vector of its middle point be $3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}),$ then the position vector of the other end is
	If G and G' be the centroids of the triangles ABC and $A'B'C'$ respectively, then $\overrightarrow{AA}'+\overrightarrow{BB'}+\overrightarrow{CC}'=$

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