Addition of Vectors | Vectors | Geometry | JEE Advanced PYQs

Addition of Vectors | Vectors | Geometry | JEE Advanced PYQs

✅ For any two points M and N in the XY-plane, let the vector from M to N be represented by MN. Let P,Q and R be three distinct points in the XY-plane. A point S lies inside triangle ΔPQR such that: In triangle PQR, a point S lies inside the triangle such that:
SP + 5·SQ + 6·SR = 0

Let E and F be the midpoints of sides PR and QR respectively.
Find the value of:

(Length of line segment EF) / (Length of line segment ES)

📚 Topic: Vectors

🔍 Subtopics: Addition of Vectors

Solution overview~

Given: SP + 5·SQ + 6·SR = 0
This implies: S divides PQ : QR : RP in 1 : 5 : 6
From this, use section formula to find coordinates of S.

E and F are midpoints of PR and QR.

Use coordinates, apply distance formula:

✅ Final Answer: 6/5

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JEE Advanced | JEE Mains | CBSE Class 12 Maths | NDA | Olympiads

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