If $a = 2i + 2j - k$ and $|xa| = 1$,then $x =$

If in the given figure $\overrightarrow{OA} = \vec{a}$,$\overrightarrow{OB} = \vec{b}$ and $AP : PB = m : n$,then $\overrightarrow{OP} = $

Let $ABCD$ be a parallelogram and $2\hat{i}+\hat{j}$,$4\hat{i}+5\hat{j}+4\hat{k}$ and $-\hat{i}-4\hat{j}-3\hat{k}$ be the position vectors of the vertices $A$,$B$,and $D$ respectively. Then the position vector of one of the points of trisection of the diagonal $AC$ is

For any two vectors $\vec{a}$ and $\vec{b}$,which of the following statements is true?

If $\vec{a}, \vec{b}, \vec{c}$ are position vectors of points $A, B, C$ respectively,with $2 \vec{a}+3 \vec{b}-5 \vec{c}=\vec{0}$,then the ratio in which point $C$ divides segment $AB$ is

If $\overrightarrow {AO} + \overrightarrow {OB} = \overrightarrow {BO} + \overrightarrow {OC} ,$ then $A, B, C$ form