If $ABCD$ is a parallelogram and the position vectors of $A, B, C$ are $i + 3j + 5k, i + j + k$ and $7i + 7j + 7k$, then the position vector of $D$ will be:

Let $\hat{i}-\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}-2 \hat{k}$ be the position vectors of points $A$ and $B$ respectively. If $C$ is a point on the line joining $A$ and $B$ such that $BC=10$,then the position vector of $C$ can be

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 $\sqrt{(|\bar{a}|+|\bar{b}|+|\bar{c}|)+|\bar{a}+\bar{b}+\bar{c}|}=$

Let $ABCDEF$ be a regular hexagon with the vertices $A, B, C, D, E$ and $F$ in counter-clockwise order. Then,the vector $\vec{AB} + \vec{BC}$ is parallel to:

If the position vector of one end of the line segment $AB$ is $2\hat{i} + 3\hat{j} - \hat{k}$ and the position vector of its midpoint is $3\,(\hat{i} + \hat{j} + \hat{k}),$ then the position vector of the other end is

In the given figure,identify which of the vectors are coinitial.