1.

Let H be the orthocenter of an acute - angled triangle ABC and O be itscircumcenter. Then vec(HA)+vec(HB)+vec(HC)

Answer»

is equal to `vec(HO)`
is equal to `vec(3HO)`
is equal to `vec(2HO)`
is not a SCALAR multiple of `vec(HO)` in general

Solution :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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