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Vector Algebra question

2025 · Shift 1 · Q25

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2025 · Shift 1 · Q25

Vector Algebra question

2025 · Shift 1 · Q25

JEE AdvancedMathematicsVector AlgebraNumerical+4 / −1

For any two points

M

and

N

in the

XY

-plane, let

\overrightarrow{MN}

denote the vector from

M

to

N

, and

\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

\triangle PQR

such that

\overrightarrow{SP} + 5\; \overrightarrow{SQ} + 6\; \overrightarrow{SR} = \vec{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 } E F}{\text { length of the line segment } E S}

is

\underline{\hspace{2cm}}

.

Numerical answer

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