If $a = (1, -1)$ and $b = (-2, m)$ are two collinear vectors,then $m = $

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=2 \hat{i}-\hat{j}+3 \hat{k}$ and $\vec{c}=\hat{i}-2 \hat{j}+\hat{k},$ find a unit vector parallel to the vector $2 \vec{a}-\vec{b}+3 \vec{c}.$

If the direction cosines of a vector of magnitude $3$ are $\frac{2}{3}, -\frac{1}{3}, \frac{2}{3}$,then the vector is:

$ABCD$ is a parallelogram such that $L$ is the mid-point of $BC$. Then,$\vec{AL}$ is equal to:

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors,then what is the maximum value of $|\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2$?

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 $x$.