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AP EAMCET202119 Aug 2021Evening ShiftMathematicsVector AlgebraActual

If i ^ + 4 j ^ + 3 k ^ , i ^ + 2 j ^ + 3 k ^ , 3 i ^ + 2 j ^ + k ^ are position vectors of A , B , C respectively and if D , E are mid points of sides B C and A C , then D E → is equal to

Options

  1. Ai ^ + j ^ + k ^
  2. Bi ^ + j ^
  3. Cj ^
  4. Dj ^ + k ^

Correct answer

C. j ^

Step-by-step solution

Given, i ^ + 4 j ^ + 3 k ^ , i ^ + 2 j ^ + 3 k ^ , 3 i ^ + 2 j ^ + k ^ are position vectors of A , B , C respectively. D is mid point of B C , then position vector of D is 1 + 3 i ^ + 2 + 2 j ^ + 3 + 1 k ^ 2 = 2 i ^ + 2 j ^ + 2 k ^ Similarly, position vector of E is 1 + 3 i ^ + 4 + 2 j ^ + 3 + 1 k ^ 2 = 2 i ^ + 3 j ^ + 2 k ^ Then, D E → = 2 i ^ + 3 j ^ + 2 k ^ - 2 i ^ + 2 j ^ + 2 k ^ = j ^ .

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