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Vectors

Blazing goIITian

Joined:	14 Jan 2007
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9 Apr 2008 22:54:59 IST

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735

Find the Least value

None

Hey,

The points represented by a(vector),b,c,d are coplarar and (sinA)a + (2sin2B)b + (3sin3C)c - 4d =0 , then the minimumm value of

sin²A +sin ²2B +sin²3C is?

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Comments (11)

srivats

Cool goIITian

Joined: 15 Mar 2008

Posts: 49

9 Apr 2008 23:33:28 IST

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The darked ones means vectors?

joy francis

Blazing goIITian

Joined: 19 Feb 2007

Posts: 1802

10 Apr 2008 17:12:19 IST

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boredom

Blazing goIITian

Joined: 14 Jan 2007

Posts: 602

10 Apr 2008 22:25:06 IST

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Hey,

sorry thats not the answer(as far as i remember)

boredom

Blazing goIITian

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10 Apr 2008 22:57:28 IST

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Hey,

please attempt..

ashish banga

Blazing goIITian

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10 Apr 2008 23:07:39 IST

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is the answer 16d² /( a² + 4b² + 9 c²)

use (Aa + Bb +Cc)²

( A² + B² + C² ) (a² + b² + c² )

ashish banga

Blazing goIITian

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10 Apr 2008 23:14:01 IST

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please reply
I AM WAITING

ashish banga

Blazing goIITian

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10 Apr 2008 23:35:48 IST

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are u there srini

boredom

Blazing goIITian

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10 Apr 2008 23:36:16 IST

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Hey,

hmmm..sorry but it is 8/7.

ashish banga

Blazing goIITian

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10 Apr 2008 23:55:59 IST

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a, b, c, d are coplanar
so we can take a = b = c = d(as any one vector can be the linesr sum of other vectors)
put in the above proved solution we can get the answer

ashish banga

Blazing goIITian

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Posts: 1362

11 Apr 2008 00:19:33 IST

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see srini there is a theorum
a and A are 2 separate quantities
and Aa is their product
like (x + 2y + 3z)^2 < 14 ( x^2 + y^2 + z^2)

Conjurer

Blazing goIITian

Joined: 20 Feb 2008

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13 Oct 2008 14:47:53 IST

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First of all, we must note that if a,b,c,d are coplanar, then (sinA)a + (2sin2B)b + (3sin3C)c - 4d will imply that sinA + 2sinB + 3sinC -4 =0

Now by Cauchy Swarz:

(sin²A +sin ²2B +sin²3C)(1 + 2^2 + 3^2) > = (sinA + 2sinB + 3sin3C)^2

=> S(14) > = (16)

=> S> = 8/7

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