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KCET2026MathematicsVector Algebra

The value of for which the vectors a = 2 i + j + k and b = i + 2 j + 3 k are orthogonal is

Options

  1. A5 2
  2. B-5 2
  3. C2 5
  4. D-2 5

Correct answer

B. -5 2

Step-by-step solution

For two vectors a and b to be orthogonal, their dot product must be zero. a b = 0 (2 i + j + k ) ( i + 2 j + 3 k ) = 0 (2)(1) + ( )(2) + (1)(3) = 0 2 + 2 + 3 = 0 2 + 5 = 0 = -5 2 Answer: -5 2

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