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AP EAMCET202421 May 2024Morning ShiftMathematicsVector AlgebraActual

a = i + j +3 k , b = j +2 k , c =3 i +2 j + k arelinearly dependent vectors and magnitude of a is 14 . If , are integers then + =

Options

  1. A3
  2. B-3
  3. C5
  4. D-5

Correct answer

A. 3

Step-by-step solution

Since a , b , c are linearly dependent. aligned & | array lll & & 3 0 & 1 & 2 3 & 2 & 1 array |=0 -3 +6 -9=0 & =2 -3 & Since | a |= 14 ^2+ ^2+9=14 & (2 -3)^2+ ^2=5 & (5 -2)( -2)=0 =2 ( 2 5 ) & =1 + =3 aligned

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