Let P(x, y) be a point on AB.
Then, the point A, P and B are collinear.
`therefore ar(triangle APB) = 0`
`rArr (1)/(2)*|[1, 2, 1],[x, y, 1],[3, 6, 1]| =0 rArr|[1, 2, 1],[x, y, 1],[3, 6, 1]| =0`
`rArr|[1, 2, 1],[x, y, 1],[0, 0, -2]| =0 " " [R_(3) to R_(3) -3R_(1)]`
`rArr (-2) *|[1, 2], [x, y]| = 0 rArr (y-2x) = 0 rArr y =2x`
Hence, the required equation is y = 2x.