If $a = \hat{i} + 4 \hat{j}$, $b = 2 \hat{i} - 2 \hat{j}$, and $c = 5 \hat{i} + 9 \hat{j}$, then $c$ is equal to:

If $A, B, C$ are the vertices of a triangle whose position vectors are $a, b, c$ and $G$ is the centroid of the $\Delta ABC$,then $\overrightarrow{GA} + \overrightarrow{GB} + \overrightarrow{GC}$ is

The perimeter of the triangle whose vertices have the position vectors $\hat{i}+\hat{j}+\hat{k}$,$5\hat{i}+3\hat{j}-3\hat{k}$,and $2\hat{i}+5\hat{j}+9\hat{k}$ is

Which of the following is not a unit vector for all values of $\theta$?

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 $P, Q, R$ are the mid-points of the sides $AB, BC$ and $CA$ of $\triangle ABC$ respectively,then $PC - BQ =$