If $\bar{a}=\bar{i}-2\bar{j}+2\bar{k}$, $\bar{b}=6\bar{i}+3\bar{j}-2\bar{k}$, and $\bar{c}=-4\bar{i}+3\bar{j}+12\bar{k}$ are three vectors, then $\sqrt{(|\bar{a}|+|\bar{b}|+|\bar{c}|)+|\bar{a}+\bar{b}+\bar{c}|}=$

The vectors $a$,$b$,and $a + b$ are:

The components of a vector $\vec{a}$ with respect to a rectangular Cartesian system are $2p$ and $1$. The system is rotated about the origin through a certain angle in the counter-clockwise direction. If the components of $\vec{a}$ with respect to the new system are $p + 1$ and $1$,then:

Represent graphically a displacement of $40 \, km$,$30^{\circ}$ east of north.

If $O$ is any point and $OA + OB + OC + OD = xOE$,where $ABCD$ is a quadrilateral and $E$ is the point of intersection of the lines joining the mid-points of opposite sides,then find the value of $x$.

If $\vec{a}=(2x+y)\hat{i}+3\hat{j}+9\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-(x-y)\hat{k}$ are two collinear vectors,then $x^3+27y^3=$