If a triangle is formed by the equations 2x+3y-1=0; x+2y-1=0; ax+by-1=0 and has its orthocentre at origin, then what are the values of a and b? (Please also tell me the Idea and steps involved in the solution)

a=8 , b =-8

solving first two lines you get the point opposite to the side formed by ax+by-1=0 .the point i s P1(-1,1).

since the origin is the orthocentre the product of slope joining P1 and oigin should be perpendicular to the variable line.

from the above condition u get the condition that a= -b .

using second and third line ,the line passing throught the point on intersection and origin is x(a-1)+y(b-2)=0 .this line is perpendicular to the first  line. this gives you the second condition u need to get values of a and b