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

Step-by-step solution

O is orthocentre and G is centroid and C is circumcentre. G divides O C in 2 :   1 ratio. Position vector of centriod G → = a → + b → + c → 3 Position vector of circum center C → = a → + b → + c → 4 Apply Section Formula, G → = 2 C → + R → 3 3 G → = 2 C → + R → R → = 3 G → - 2 C → = ( a → + b → + c → ) - 2 a → + b → + c → 4 = a → + b → + c → 2