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AP EAMCET20226 Jul 2022Morning ShiftMathematicsVector AlgebraActual

Let a =2 i +3 j + k , b =4 i + j , c = i -3 j -7 k . If r =x i +y j +z k , r a =9, r b =7, r c =6 then (x, y, z)=

Options

  1. A(1,-3,2)
  2. B(-1,3,-2)
  3. C(1,3,2)
  4. D(1,3,-2)

Correct answer

D. (1,3,-2)

Step-by-step solution

Given a =2 i +3 j + k , b =4 i + j , c = i -7 k Here, r a =9 . and (2 i +3 j + k )=9 Similarly, r b =7 and r c =6 aligned & 4 x+y=7 ...(ii) & x-3 y-7 z=6...(iii) aligned Multiply eq. (i) by 7 14 x+21 y+7 z=63...(iv) Add (iii) and (iv) aligned & 14 x+21 y+7 z=63 & x-3 y-7 z=6 & 15 x+18 y=69 & 5 x+6 y=23...(v) aligned Multiply equation (ii) by b . aligned 24 x+6 y & =42 5 x 6 y & =23 19 x & =19 aligned x=1 From (ii), gathered 4 x+y=7 4+y=7 y=3 gathered From (i) aligned & 2 x +3 y + z : 9 2 1+3 3+2=9 & z =9-2-9=-2 ali

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