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AP EAMCET202315 May 2023Morning ShiftMathematicsVector AlgebraActual

Let OA =2 i -3 j + k , OB = i -4 j -3 k and OC =-3 i + j +2 k be the position vectors of three points, A , B , C respectively. If G is the centroid of triangle ABC , then BC ^2+ CA ^2+ AB ^2+9( OG )^2=

Options

  1. A162
  2. B156
  3. C144
  4. D132

Correct answer

A. 162

Step-by-step solution

aligned & Position vector of centroid = OG = OA + OB + OC 3 & OG =-2^ aligned Now BC = OC - OB =-4 i +5 j +5 k aligned & CA = OA - OC =-5 i -4 j - k & AB = OB - OA =- i - j -4 k aligned Therefore aligned & BC ^2+ CA ^2+ AB ^2+9( OG )^2= BC BC + CA CA + AB AB & +9( OG OG ) aligned aligned & =66+42+18+9 & =162 aligned

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