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AP EAMCET20227 Jul 2022Evening ShiftMathematicsVector AlgebraActual

If a = i +2 j +3 k , b =2 i +3 j + k , c =8 i +13 j +9 k and x a +y b +z c =0 , then x y z^2 =

Options

  1. A-1
  2. B-6
  3. C6
  4. D1-8 i -12 j +24 k

Correct answer

C. 6

Step-by-step solution

aligned & x a +y b +z c =0 & (x+2 y+8 z) i +(2 x+3 y+13 z) j & +(3 x+y+9 z) k =0 & x+2 y+8 z=0 & 2 x+3 y+13 z=0 & 3 x+y+9 z=0 aligned From Eqs. (i) and (ii), aligned & -y-3 z=0 y=-3 z & x-6 z+8 z=0 & x=-2 z & x y z^2 = (-2 z)(-3 z) z^2 =6 & aligned

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