Let H be the orthocenter of an acute - angled triangle ABC and O be itscircumcenter. Then `vec(HA)+vec(HB)+vec(HC)`A. is equal to `vec(HO)`B. is equal to `vec(3HO)`C. is equal to `vec(2HO)`D. is not a scalar multiple of `vec(HO)` in general

Let H be the orthocenter of an acute - angled triangle ABC and O be it

1.	Let H be the orthocenter of an acute - angled triangle ABC and O be itscircumcenter. Then `vec(HA)+vec(HB)+vec(HC)`A. is equal to `vec(HO)`B. is equal to `vec(3HO)`C. is equal to `vec(2HO)`D. is not a scalar multiple of `vec(HO)` in general
Answer» Correct Answer - C G ic centroid `G=(A+B+C)/(3)` `G=(20+H)/(3)` `2O+H=3G` `vec(HA)+vec(HB)+vec(HC)=vec(A)-vec(H)-vec(B)+vec(C)-vec(H)` `=vec(A)+vec(B)+vec(C)-3vec(H)` `=3vec(G)-3vec(H)` `=2vec(O)+vecH-3vec(H)` `=2vec(O)-2vec(H)` `=2vec(HO)`

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Let H be the orthocenter of an acute - angled triangle ABC and O be itscircumcenter. Then `vec(HA)+vec(HB)+vec(HC)`A. is equal to `vec(HO)`B. is equal to `vec(3HO)`C. is equal to `vec(2HO)`D. is not a scalar multiple of `vec(HO)` in general

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