If $p = (7, -2, 3)$ and $q = (3, 1, 5)$,then the magnitude of $p - 2q$ is $......$.

If three points $A$,$B$,and $C$ have position vectors $(1, x, 3)$,$(3, 4, 7)$,and $(y, -2, -5)$ respectively and if they are collinear,then $(x, y)$ is

Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $(2 \vec{a}+\vec{b})$ and $(\vec{a}-3 \vec{b})$ externally in the ratio $1:2$. Also,show that $P$ is the mid-point of the line segment $RQ$.

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:

$<2, 2, 2> = \ldots \ldots$

Let $ABCDEF$ be a regular hexagon with the vertices $A, B, C, D, E, F$ in counterclockwise order. Then the vector $\vec{AB} + \vec{AF} + \vec{CD} + \vec{EF}$ is equal to