If O is the circumcentre and P the orthocentre of `/_\ABC`, prove that `vec(PA)+vec(PB)+vec(PC)=2vec(OP)`

If O is the circumcentre and P the orthocentre of Delta ABC , prove that vec(OA)+ vec(OB) + vec(OC) =vec(OP) .

If O is the circumcentre, G is the centroid and O' is orthocentre or triangle ABC then prove that: vec(OA) +vec(OB)+vec(OC)=vec(OO')

If S is the cirucmcentre, G the centroid, O the orthocentre of a triangle ABC, then vec(SA) + vec(SB) + vec(SC) is:

If AD, BE and CF be the median of a /_\ABC , prove that vec(AD)+vec(BE)+vec(CF) =0

In a parallelogram ABCD. Prove that vec(AC)+ vec (BD) = 2 vec(BC)

If O\ a n d\ O^(prime) are circumcentre and orthocentre of \ A B C ,\ t h e n\ vec O A+ vec O B+ vec O C equals a. 2 vec O O ' b. vec O O ' c. vec O ' O d. 2 vec O ' O

If C is the mid point of AB and P is any point outside AB then (A) vec(PA)+vec(PB)+vec(PC)=0 (B) vec(PA)+vec(PB)+2vec(PC)=vec0 (C) vec(PA)+vec(PB)=vec(PC) (D) vec(PA)+vec(PB)=2vec(PC)

If C is the mid point of AB and P is any point outside AB then (A) vec(PA)+vec(PB)+vec(PC)=0 (B) vec(PA)+vec(PB)+2vec(PC)=vec0 (C) vec(PA)+vec(PB)=vec(PC) (D) vec(PA)+vec(PB)=2vec(PC)

If C is the mid point of AB and P is any point outside AB then (A) vec(PA)+vec(PB)+vec(PC)=0 (B) vec(PA)+vec(PB)+2vec(PC)=vec0 (C) vec(PA)+vec(PB)=vec(PC) (D) vec(PA)+vec(PB)=2vec(PC)

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are vec(a) , vec(b) , vec(c ) and (vec(a) + vec(b) + vec(c ))/(4) respectively, then the position vector of the orthocentre of this triangle is