In a quadrilateral $PQRS$, $A$ divides $SR$ in the ratio $1:3$ and $B$ is the mid-point of $PR$. If $3SR - QR - 3PS - PQ = kAB$, then $k=$

If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar,then $\lambda \vec{a}$ is a unit vector if

If $O$ is the origin and $C$ is the midpoint of $A(2, -1)$ and $B(-4, 3)$,then the value of $\overrightarrow{OC}$ is:

The position vectors of three points $A, B$ and $C$ are $(1, 3, x), (3, 5, 8)$ and $(y, -1, -6)$ respectively. If $A, B$ and $C$ are collinear, then $(x, y) =$

The vectors $b$ and $c$ are in the direction of north-east and north-west respectively and $|b| = |c| = 4$. The magnitude and direction of the vector $d = c - b$ are:

Let $ABCD$ be a quadrilateral. If $E$ and $F$ are the midpoints of the diagonals $AC$ and $BD$ respectively and $(\overrightarrow{AB}-\overrightarrow{BC})+(\overrightarrow{AD}-\overrightarrow{DC})= k \overrightarrow{FE}$,then $k$ is equal to