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Orthocenter of an equilateral triangle A...

Orthocenter of an equilateral triangle ABC is the origin O. If `vec(OA)=veca, vec(OB)=vecb, vec(OC)=vecc`, then `vec(AB)+2vec(BC)+3vec(CA)=`

A

`3vec(c)`

B

`3vec(a)`

C

0

D

`3vec(b)`

Text Solution

Verified by Experts

The correct Answer is:
B
For an equilateral triangle, centroid is the samme as orthocentre
`therefore(OA+OB+OC)/(3)=0`
`thereforeOA+OB+OC=0`
Now, `AB+2BC+3CA`
`=OB-OA+2OC-2OB+3OA-3OC`
`=-OB+2OA-OC`
`=(OB+OA+OC)+3OA=3OA=3a`
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