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17 Sep 2009 14:09:57 IST

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A,B,C ARE THREE NON COLLINEAR PONITS WITH POSITION VECTORS a,b,c respectively given P,Q,R are ponit

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A,B,C ARE THREE NON COLLINEAR PONITS WITH POSITION VECTORS a,b,c respectivelygiven P,Q,R are ponits on BC,CA&AB respectively such that:BP:PC=CQ:QA=AR:RB=1:2Find the position vectors of the vertices of the triangle XYZ formed lines AB,BQ,CR.hence show that the centroid of tiangle ABC is same as that of triangle XYZ slove with diag.

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Prathamesh Mayekar

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Joined: 12 Nov 2011

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12 Nov 2011 12:06:39 IST

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Hi Saurabh I`ve gt a quick soln to ur problem is very simple u see,Draw a triangle with Vertices ABC and pts P,Q & R dividing sides BC,AB & AC in the ratio 1:2, Now, from the section formula for internal division,q^=1b^+2a^/3 =i^+j^+k^+2i^+2j^+2k^/3=3i+3j+3k/3=i+j+kSimilarly u get the pv`s p & q as i+j+k. Now, for centriod by Centroid formula,for tr.ABC g^=a+b+c/3=i+j+kwhichi is equal 2 the g for tr.pqr[NOTE:THE TRIANGLE FORME BY THE POINTS IS PQR AND NOT XYZ(or you might hav put the question worong as there is no triangle existing between AB.BQ n CR as AB n BQ r on the same side]Hope this helps you! :) :)

Prathamesh Mayekar

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Joined: 12 Nov 2011

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12 Nov 2011 12:06:49 IST

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