AP EAMCET2010MathematicsVector Algebra

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

Options

A2 16-( a b )^2
B16-( a b )^2
C2 4-( a b )^2
D4-( a b )^2

Correct answer

A. 2 16-( a b )^2

Step-by-step solution

We have, u = a - b , v = a + b u v =( a - b ) ( a + b )=0- b a + a b -0=2 a b | u v |=2| a b |=2 | a b |^2 =2 | a |^2| b |^2 ^2 | n |^2 n = unit vector | n |=1 =2 4 4 ^2 1 =2 16 (1- ^2 ) =2 16-16 ^2 =2 16-16 ( a b | a || b | )^2 a b =| a || b | =2 16-16 ( a b )^2 | a |^2| b |^2 =2 16-16 ( a b )^2 4 4 2 16-( a b )^2

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