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AP EAMCET202315 May 2023Morning ShiftMathematicsVector AlgebraActual

a and b are two vectors such that a is not parallel to b . If p =( x +2 y +3) a +(5 x - y +2) b and q =(2 x +3 y +5) a +(x-5 y-2) b are two vectors such that p =2 q , then x -2 y =

Options

  1. A3
  2. B2
  3. C-2
  4. D-3

Correct answer

B. 2

Step-by-step solution

aligned & p =2 q & (x+2 y+3) a +(5 x-y+2) b & (4 x+6 y+10) a +(2 x-10 y-9) b aligned Comparing both sides we get aligned & 3 x+4 y+7=0 ...(1) & and 3 x+9 y+6=0 ...(2) aligned Solving (1) & (2) we get, x=- 13 5 , y= 1 5 Hence x-2 y=-3

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