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COMEDK20269 May 2026Evening ShiftMathematicsVector AlgebraActual

If ( a + b ) b and ( a + 2 b ) a , then

Options

  1. A| a | = 2 | b |
  2. B| a | = 2| b |
  3. C2| a | = | b |
  4. D| a | = | b |

Correct answer

A. | a | = 2 | b |

Step-by-step solution

Given ( a + b ) b , taking the dot product with b gives zero: ( a + b ) b = 0 a b + | b |^2 = 0 a b = -| b |^2 Also given ( a + 2 b ) a , taking the dot product with a gives zero: ( a + 2 b ) a = 0 | a |^2 + 2( a b ) = 0 Substituting the value of a b from the first equation: | a |^2 + 2(-| b |^2) = 0 | a |^2 = 2| b |^2 | a | = 2 | b | Answer: | a | = 2 | b |

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