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COMEDK2018MathematicsVector Algebra

If u = a - b , v = a + b , and | a |=| b |=2 , then | u v | is

Options

  1. A2 16-( a b )²
  2. B2 4-( a b )²
  3. C16-( a b )²
  4. D4-( a b )²

Correct answer

A. 2 16-( a b )²

Step-by-step solution

Given that, u = a - b , v = a + b and | a |=| b |=2 Now, | u v |=| a - b a + b |=2( a b )=2| a || b | =2 2 2 =8 =8 1- ² =8 1- ( a b |a||b| )² =8 1- ( a b 4 )² =8 1- ( a b 16 )² = 8 4 16-(a b)² =2 16-(a b)²

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