The vertices of a ΔABC are A(1,0,0),B(0,2,0),C(0,0,3) . If a,b,-111 are the direction  ratios of the line joining the orthocenter and circumcentre of ΔABC then a+b=

The equation of plane ABC is x1+y2+z3=1 if H(α,β,γ) is the orthocenter then AH⊥BC,BH⊥CA⇒α=2β=3γH lies in the plane of triangle ABC then α1+α4+α9=1⇒α=3649 ∴H=3649,1849,1249 The circum center, orthocenter, centroid are collinear and centroid (G)=13,23,1 The dr'sof HG,3649-13,1849-23,1249-1=59,-44,-111a=59,b=-44⇒a+b=15