Mathematics - Vector Question with Solution | TestHub

For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\overrightarrow{0}$ 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 $△PQR$ such that $\overrightarrow{SP}+5\overrightarrow{SQ}+6\overrightarrow{SR}=\overrightarrow{0}$. Let $E$ and $F$ be the mid-points of the sides $PR$ and $QR$, respectively. Then the value of $\frac{\text{ length of the line segment }EF}{\text{ length of the line segment }ES}$ is ________