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MHT CET202313 May 2023Evening ShiftMathematicsVector AlgebraActual

a =2 i +3 j +4 k , b = i -2 j + k , c = i + j - k are three vectors. For a vector r with r a = b and r c =3,| r | is

Options

  1. A55
  2. B155
  3. C138
  4. D170

Correct answer

B. 155

Step-by-step solution

aligned & Let r =x i +y j + z k & r a = b & | array llr i & j & k x & y & z 2 & 3 & 4 array |= b & (4 y-3 z ) i -(4 x-2 z ) j +(3 x-2 y) k = i -2 j + k aligned . array r 4 y-3 z=1 4 x-2 z=2 3 x-2 y=1 array ) ...(i) aligned & r c =3 & (x i +y j + z k ) ( i + j - k )=3 aligned x+y-z=3 ...(ii) x=5, y=7, z=9 aligned r = & 5 i +7 j +9 k | r | & = 5^2+7^2+9^2 & = 155 aligned

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