Vector Algebra

For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\vec{0}$ denote the zero vector. Let $P, Q$ and $R$ be three distinct points in the $XY$-plane. Let $S$ be a point inside the triangle $\triangle PQR$ such that

\(\overrightarrow{SP} + 5\; \overrightarrow{SQ} + 6\; \overrightarrow{SR} = \vec{0}.\)

Let $E$ and $F$ be the mid-points of the sides $PR$ and $QR$, respectively. Then the value of

$\frac{\text { length of the line segment } E F}{\text { length of the line segment } E S}$

is ________________.