JEE Advanced2012MathematicsVector AlgebraActual

If a , b and c are unit vectors satisfying | a - b |²+| b - c |²+| c - a |²=9 , then |2 a +5 b +5 c | is

Correct answer

Step-by-step solution

array l | a |=| b |=| c |=1 | a - b |²+| b - c |²+| c - a |²=9 2 (| a |²+| b |²+| c |² )-2( a b + b c + c a )=9 a b + b c + c a = -3 2 array Also, array l | a + b + c |²=| a |²+| b |²+| c |²+2( a b + b c + c a ) =1+1+1+2 (- 3 2 )=0 a + b + c =0 ( b + c )=- a |2 a +5( b + c )|=|2 a -5 a |=|-3 a |=3 array

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