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(Solved): The figure shows the acute-angled triangle ABC.G and O are the centroid and the orthocentre of /_( ...


The figure shows the acute-angled triangle

ABC.G

and

O

are the centroid and the orthocentre of

/_(/)ABC

respectively. Let

vec(OA)=a,vec(OB)=b

and

vec(OC)=c

. (a) Show that

vec(OG)=(1)/(3)a+(1)/(3)b+(1)/(3)c

(b) If

BG_(|)_(A)C

, show that

B,G

and

O

are collinear.



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