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AP EAMCET202316 May 2023Morning ShiftMathematicsVector AlgebraActual

If a =(2 x+y) i +3 j +9 k and b =2 i + j -(x-y) k are two collinear vectors, then x^3+27 y^3=

Options

  1. A1241
  2. B1512
  3. C1072
  4. D1729

Correct answer

D. 1729

Step-by-step solution

Given: a =(2 x+y) i +3 j +9 k b =2 i + j -(x-y) k a and b are co-linear vectors 2 x+y 2 = 3 1 = 9 -(x-y) 2 x+y 2 = 3 1 2 x+y=6 ...(i) and 3 1 = 9 y-x y-x=3 ...(ii) Solving eqns. (i) and (ii), we get x=1 and y=4 Now, x^3+27 y^3=1+27 64=1729 .

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