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JEE Advanced2025MathematicsVector AlgebraActual

For any two points M and N in the X Y -plane, let M N denote the vector from M to N , and 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 P Q R such that S P +5 S Q +6 S R = 0 . Let E and F be the mid-points of the sides P R and Q R , respectively. Then the value of length of the line segment E F length of the line segment E S is ________

Correct answer

0

Step-by-step solution

aligned & SP +5 SQ +6 SP = 0 & (Let P.V. of P be p , Q be q and R be r ) & aligned & ( p - s )+5( q - s )+6( r - s )= 0 & S = p +5 q +6 r 12 & E F = ( q - p 2 ) & E S = ( 5 q -5 p 12 )= 5 12 ( q - p ) & | E F | | E S | = 6 5 =1.2 aligned aligned

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