If $a = (2, 5)$ and $b = (1, 4),$ then the vector parallel to $(a + b)$ is

If $ABCDEFGH$ is a convex octagon,then $\vec{AB} + \vec{BC} + \vec{CD} + \vec{DE} + \vec{AH} + \vec{HG} + \vec{GF} + \vec{FE} = $

The number of unit vectors of the form $a \hat{i} + b \hat{j} + c \hat{k}$,where $a, b, c \in W$ is

If $a + b$ bisects the angle between $a$ and $b$,then $a$ and $b$ are

If $\hat{i}+4 \hat{j}+3 \hat{k}$,$\hat{i}+2 \hat{j}+3 \hat{k}$,and $3 \hat{i}+2 \hat{j}+\hat{k}$ are position vectors of $A$,$B$,and $C$ respectively,and if $D$ and $E$ are midpoints of sides $BC$ and $AC$,then $\overrightarrow{DE}$ is equal to:

$ABCD$ is a parallelogram and $P$ is the mid-point of the side $AD$. The line $BP$ meets the diagonal $AC$ in $Q$. Then, the ratio of $AQ:QC$ is equal to