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

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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 ________

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Correct answer: A. A

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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