JEE Advanced 2025 Paper 1 Mathematics Q9

Mathematics

Problem

For any two points M and N in the XY-plane, let MN⃗\vec{N} denote the vector from M to N, and 0⃗\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 ΔPQR such that SP⃗\vec{P} + 5SQ⃗\vec{Q} + 6SR⃗\vec{R} = 0⃗\vec{0}. Let E and F be the mid-points of the sides PR and QR, respectively. Then the value of (length of the line segment EF)/(length of the line segment ES) is _______________.

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