Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

If a , b and c are unit vectors, then find the maximum value of |2 a -3 b |^2+|2 b -3 c |^2+|2 c -3 a |^2

Correct answer

Step-by-step solution

Let y=|2 a -3 b |^2+|2 b -3 c |^2+|2 c -3 a |^2 aligned & y =3(4+9)-12( a ~b + b c + c a ) & y =39-12( a ~b + b c + c a ) ...(1) aligned aligned & [ array l As | a + b + c |^2 0 3+2( a b + b c + c a ) 0 a b + b c + c a -3 2 array ] & y_ =39+(12) ( 3 2 )=39+18=57 Ans. aligned Now y will be maximum if value of a b is minimum i.e. equal to - 3 2

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