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Question

If A,B,C are the vertices of a triangle whose position vectors are a,b,c and G is the centroid of the ABC, then GA+GB+GC is

A
0
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B
A+B+C
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C
a+b+c3
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D
abc3
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Solution

The correct option is A 0
Given the position vectors of vertices A,B and C of the triangle ABC are a,b and c

ie OA=aOB=bOC=c

Centroid of triangle (G)=a+b+c3

Now GA+GB+GC

=(OAOG)+(OBOG)+(OCOG)

=(aa+b+c3)+(ba+b+c3)+(ca+b+c3)

=13(3aabc+3babc+3cabc)

=13[0]=0

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