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G is the centriod of triangle ABC and if G1 is the centriod of another triangle A1B1C1 show vector AA1 + vector BB1 + vector CC1 = 3 vector GG1.

G is the centriod of triangle ABC and if G1 is the centriod of another triangle A1B1C1 show vector AA1 + vector BB1 + vector CC1 = 3 vector GG1. 

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
 

let O is the origin

then OG  =( OA +OB +OC)/3

 

and OG’ = (OA' + OB ' OC')/3

 

subtract

  OG -OG'=  ( OA +OB +OC)/3 - (OA' + OB ' OC')/3   

 GG'  = (AA' + BB' + CC')/3

AA`+BB`+CC`= 3GG'

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