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Vectors

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5 Dec 2011 08:33:12 IST

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Vectors

Mathematics

If a,b,c are unit vectors, then the maximum value of |5a-7b|^2+|5b-7c|^2+|5c-7a|^2 is?

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Arjun Virmani

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Joined: 1 Jun 2009

Posts: 1294

26 Dec 2011 19:59:46 IST

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The square of modulus is actually the dot product of the vector with itself!!!!!

and as we can see in these vectors we have - sign!!!

lets take one of these..

|5a-7b|^2 = (5a-7b).(5a-7b) = 25 a.a +49 b.b - 35 a.b - 35 b.a = 25 a.a +49 b.b - 2*35 a.b..............[as a.b =b.a]

we can see that these open simply as (a-b)^2...........

A fact :

Angle between two vectors in free space can never b greater than 180(degrees) or pie radians!!!!!

therefore in free space the dot product of 2 vectors can never b -ve...............

and therefore, in this case, to maximize the output we can put it zero!!

so the result is 74.......... [a.a = b.b = 1 {unit vectors}]!!

thrfr, 74 +74 +74 = 222!!! ans!!

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