Questions in vectors-m

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If O be the circumcentre and O' be the orthocentre of the triangle ABC, then $\overrightarrow{O'A}+\overrightarrow{O'B}+\overrightarrow{O'C}=$
If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by $\overrightarrow{AE}$ will be
The position vector of a point C with respect to B is $\mathbf{i}+\mathbf{j}$ and that of B with respect to A is $\mathbf{i}-\mathbf{j}.$ The position vector of C with respect to A is
A and B are two points. The position vector of A is $6\mathbf{b}-2\mathbf{a}.$ A point P divides the line AB in the ratio 1 : 2. If $\mathbf{a}-\mathbf{b}$ is the position vector of P, then the position vector of B is given by
If the position vectors of the points A and B are $c=(2\,-2,\,4)$ and $3\mathbf{i}-\mathbf{j}-3\mathbf{k},$ then what will be the position vector of the mid point of AB
If C is the middle point of AB and P is any point outside AB, then
If in a triangle $\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{b}$ and D, E are the mid-points of AB and AC respectively, then $\overrightarrow{DE}$ is equal to
In the triangle ABC, $\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{c},\,\,\overrightarrow{BC}=\mathbf{b}$ , then
ABCDE is a pentagon. Forces $\overrightarrow{AB},\,\overrightarrow{AE},\,\overrightarrow{DC},\,\overrightarrow{ED}$ act at a point. Which force should be added to this system to make the resultant ${{\cos }^{-1}}\frac{4}{5}$
Let A and B be points with position vectors a and b with respect to the origin O. If the point C on OA is such that $2AC=CO,\,\,CD$ is parallel to OB and $|\overrightarrow{CD}|\,\,=\,\,3|\overrightarrow{OB}|,$ then $\overrightarrow{AD}$ is equal to

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