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. `3vecc`B. `3veca`C. `vec0`D. `3vecb`

Orthocenter of an equilateral triangle ABC is the origin O. If `vec(OA

1.	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. `3vecc`B. `3veca`C. `vec0`D. `3vecb`
Answer» Correct Answer - B For an equilateral triangle, centroid is the same as orthocenter `therefore (vec(OA) + vec(OB) + vec(OC))/(3) =vec0` `therefore vec(OA)+vec(OB)+vec(OC) =vec0` Now, `vec(AB) + 2vec(BC) + 3vec(CA)` `=vec(OB) - vec(OA) +2vec(OC) - 2vec(OB) + 3vec(OA)-3vec(OC)` `=-vec(OB) + 2vec(OA) -vec(OC)` `=-(vec(OB) +vec(OA) +vec(OC))+3vec(OA)` `=3vec(OA)` `=3veca`

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