$A, B, C, D$ are any four points. If $E$ and $F$ are midpoints of $AC$ and $BD$ respectively, then $\vec{AB} + \vec{CB} + \vec{CD} + \vec{AD} =$

If $a, b, c$ are any vectors,then the true statement is

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

If $a = 3i - 2j + k$,$b = 2i - 4j - 3k$,and $c = -i + 2j + 2k$,then $a + b + c = \dots$

The position vectors of two points $A$ and $B$ are $\bar{i}+2\bar{j}+3\bar{k}$ and $7\bar{i}-\bar{k}$ respectively. The point $P$ with position vector $-2\bar{i}+3\bar{j}+5\bar{k}$ is on the line $AB$. If the point $Q$ is the harmonic conjugate of $P$ with respect to $A$ and $B$, then the sum of the scalar components of the position vector of $Q$ is

$A$ line segment $PQ$ has the length $63$ and direction ratios $(3, -2, 6)$. If this line makes an obtuse angle with the $X$-axis,then the components of the vector $\vec{PQ}$ are