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AP EAMCET201825 Apr 2018Morning ShiftMathematicsVector AlgebraActual

If a → = i ^ + j ^ + k ^ , b → = 2 i ^ - j ^ + 3 k ^ and c → = i ^ - j ^ and if 6 i ^ + 2 j ^ + 3 k ^ = λ 1 ( a → × b → ) + λ 2 ( b → × c → ) + λ 3 ( c → × a → ) , then λ 1 , λ 2 , λ 3 =

Options

  1. A11 5 , 4 5 , 19 5
  2. B4 5 , 19 5 , 11 5
  3. C4 5 , 11 5 , 19 5
  4. D19 5 , 11 5 , 4 5

Correct answer

C. 4 5 , 11 5 , 19 5

Step-by-step solution

Given a → = i ^ + j ^ + k ^ b → = 2 i ^ - j ^ + 3 k ^ c → = i ^ - j ^ Now, a → × b → = i ^ j ^ k ^ 1 1 1 2 - 1 3 = 4 i ^ - j ^ - 3 k ^ b → × c → = i ^ j ^ k ^ 2 - 1 3 1 - 1 0 = 3 i ^ + 3 j ^ - k ^ Similarly, c → × a → = - i ^ - j ^ + 2 k ^ Now we have 6 i ^ + 2 j ^ + 3 k ^ = λ 1 ( a → × b → ) + λ 2 ( b → × c → ) + λ 3 ( c → × a → ) = λ 1 4 i ^ - j ^ - 3 k ^ + λ 2 3 i ^ + 3

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