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ABC is an equilateral triangle. Length o...

ABC is an equilateral triangle. Length of each side is 'a' and centroid is point O. Find

If `vec(AB)+vec(AC)=nvec(AO)` then n = ?

Text Solution

Verified by Experts

The correct Answer is:
3
`vec(AB)=vec(AO)+vec(OB)andvec(AC)=vec(AO)+vec(OC)therefore vec(AB)+vec(AC)=2vec(AO)+vec(OB)+vec(OC)....(1)`
but `vec(OA)+vec(OB)+vec(OC)=vec(0) therefore vec(OB)+vec(OC)=-vec(OA)=vec(AO)....(2)`
by (1) and (2) `vec(AB)+vec(AC)=2vec(AO)+vec(AO)" "vec(AB)+vec(AC)=3vec(AO) therefore n=3`
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