If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x + y = 1, then the orihocenire of the triangle is

Let OAB be the equilateral triangle. In an equilateral triangle the orthocentre and centroid coincide. So, the orthocentre H divides OL in the ratio 2: 1. OL = Length of the L from (0, 0) on x + y -1= 0⇒ OL=12∴ OH=23×OL=23So, the coordinates of Hare23cos⁡π4,23sin⁡π4≡(1/3,1/3)