The projections of a vector on the three coordinate axes are $6, -3, 2$ respectively. The direction cosines of the vector are:

If $D, E$ and $F$ are respectively the mid-points of $AB, AC$ and $BC$ in $\triangle ABC$, then $\overrightarrow{BE} + \overrightarrow{AF}$ is equal to :

If $M_1, M_2, M_3$ and $M_4$ are respectively the magnitudes of the vectors $\vec{a}_1 = 2\hat{i} - \hat{j} + \hat{k}$,$\vec{a}_2 = -3\hat{i} - 4\hat{j} - 4\hat{k}$,$\vec{a}_3 = -\hat{i} + \hat{j} - \hat{k}$,and $\vec{a}_4 = -\hat{i} + 3\hat{j} + \hat{k}$,then the correct order of $M_1, M_2, M_3$ and $M_4$ is:

Let $u$ and $v$ be two vectors. Then $|u-v|=||u|-|v||$ if and only if

If vectors $a$ and $b$ represent two consecutive sides of a regular hexagon,then the vectors representing the remaining four sides in order are:

If $\vec{a}$ and $\vec{b}$ are the position vectors $(P.V.)$ of two points $A$ and $B$ respectively,and $C$ divides the line segment $AB$ in the ratio $2 : 1$,then the position vector of $C$ is: