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KCET2026MathematicsVector Algebra

If a = 2 i + 2 j - k , b = i + j + 2 k and | a + b | = | a - b | , then + is equal to

Options

  1. A2
  2. B-1
  3. C0
  4. D1

Correct answer

D. 1

Step-by-step solution

Given | a + b | = | a - b | Squaring both sides: | a |^2 + | b |^2 + 2 a b = | a |^2 + | b |^2 - 2 a b 4 a b = 0 a b = 0 Substituting the given vectors a = 2 i + 2 j - k and b = i + j + 2 k : (2)( ) + (2)( ) + (-1)(2) = 0 2 + 2 - 2 = 0 2( + ) = 2 + = 1 Answer: 1

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