JEE Advance 2025 Paper 1

Let $P, Q, R$   be distinct points in the xy-plane. Let $S$   be a point inside $\Delta PQR$   such that $\vec{SP} + 5\vec{SQ} + 6\vec{SR} = \vec{0}$  . Let $E$   and $F$   be the mid-points of $PR$   and $QR$  . Find the ratio of the length of segment $QS$   to the length of segment $EF$  .