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AP EAMCET2006MathematicsVector Algebra

a i = a (2 i + j )= a ( i + j +3 k )=1 , then a is equal to :

Options

  1. Ai - k
  2. B1 / 3(3 i +3 j + k )
  3. C1 / 3( i + j + k )
  4. D1 / 3(3 i -3 j + k )

Correct answer

D. 1 / 3(3 i -3 j + k )

Step-by-step solution

Let a =a₁ i +a₂ j +a₃ k a i =1 (a₁ i +a₂ j +a₃ k ) i =1 a₁=1 Now, a (2 i + j )=1 (a₁ i +a₂ j +a₃ k ) (2 i + j )=1 2 a₁+a₂=1 a₂=1-2 ( a₁=1 ) a₂=-1 and a ( i + j +3 k )=1 (a₁ i +a₂ j +a₃ k ) ( i + j +3 k )=1 a₁+a₂+3 a₃=1 1-1+3 a₃=1 a₃= 1 3 a = i - j + 1 3 k = 1 3 (3 i -3 j + k )

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