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If $D,\,E,\,F$ are respectively the mid points of $AB,\,AC$ and $BC$ in $\Delta ABC$ , then $\overrightarrow{BE}$ $+\overrightarrow{AF}=$
If $4\mathbf{i}+7\mathbf{j}+8\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j}+4\mathbf{k}\,$ and $2\mathbf{i}+5\mathbf{j}+7\mathbf{k}$ are the position vectors of the vertices A, B and C respectively of triangle ABC. The position vector of the point where the bisector of angle A meets BC is
If $\mathbf{a}=\mathbf{i}-\mathbf{j}$ and $\mathbf{b}=\mathbf{i}+\mathbf{k}$ , then a unit vector coplanar with $\mathbf{a}$ and $\mathbf{a}$ and perpendicular to $\mathbf{a}$ is
If the position vectors of the points A, B, C be $\mathbf{i}+\mathbf{j},\,\,\,\mathbf{i}-\mathbf{j}$ and $a\,\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}$ respectively, then the points A, B, C are collinear if
If the points $\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}$ and $\mathbf{a}+k\,\mathbf{b}$ be collinear, then k =
If the position vectors of the points A, B, C be $\mathbf{a},\ \mathbf{b}$ , $3\mathbf{a}-2\mathbf{b}$ respectively, then the points A, B, C are
If a, b, c are non-collinear vectors such that for some scalars x, y, z, $x\mathbf{a}+y\mathbf{b}+z\mathbf{c}=\mathbf{0},$ then
The vectors $3\,\mathbf{i}+\mathbf{j}-5\,\mathbf{k}$ and $a\,\mathbf{i}+b\,\mathbf{j}-15\,\mathbf{k}$ are collinear, if
The points with position vectors $60\,\mathbf{i}+3\,\mathbf{j}$ , $40\,\mathbf{i}-8\mathbf{j},$ , $a\,\mathbf{i}-52\,\mathbf{j}$ are collinear, if $a=$
If O be the origin and the position vector of A be $4\,\mathbf{i}+5\,\mathbf{j},$ then a unit vector parallel to $\overrightarrow{OA}$ is

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