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JEE MainMathematicsVector Algebra

Let a = 2 i - j + 3 k and c = i + j + k , where , Z . If there exists at least one vector b such that b a = c and | c | = 3 3 , then the value of + is

Options

  1. A-4
  2. B6
  3. C-6
  4. D4

Correct answer

B. 6

Step-by-step solution

Given b a = c , the vector c must be perpendicular to a . Therefore, c a = 0 . (2 i - j + 3 k ) ( i + j + k ) = 0 2 - + 3 = 0 = 2 + 3 It is also given that | c | = 3 3 , so | c |^2 = 27 . ^2 + ^2 + 1^2 = 27 ^2 + ^2 = 26 Substituting = 2 + 3 into the equation: ^2 + (2 + 3)^2 = 26 ^2 + 4 ^2 + 12 + 9 = 26 5 ^2 + 12 - 17 = 0 (5 + 17)( - 1) = 0 Since is an integer, = 1 . Then, = 2(1) + 3 = 5 . The value of + = 1 + 5 = 6 . Answer: 6

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