For any two points M and N in the X Y-plane, let \overrightarrow{M N} 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 X Y-plane. Let S be a point inside the triangle \triangle P Q R such that \overrightarrow{S P}+5 \overrightarrow{S Q}+6 \overrightarrow{S R}=\overrightarrow{0} Let E and F be the mid-points of the sides P R and Q R, respectively. Then the value of {\text{ length of the line segment } E F}/{\text{ length of the line segment } E S} is_____ . [JEE Adv 2025 P1]

Vector Algebra

Section: Mathematics

Question : 3 of 38

Marks: +1, -0

For any two points M and N in the XY-plane, let

→

denote the vector from M to N, and

→

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

→

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_____ .

[JEE Adv 2025 P1]

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