# In a quadrilateral $ABCD,$ the point P divides DC in the ratio $1:2$ and Q is the mid point of AC.If $\overrightarrow {AB}+2 \overrightarrow {AD}+\overrightarrow {BC}-2 \overrightarrow {DC}=k \overrightarrow {PQ}$, then $k=$

$\begin {array} {1 1} (1)\;-6 & \quad (2)\;-4 \\ (3)\;6 & \quad (4)\;4 \end {array}$

(1) -6