Find the foot of the perpendicular onto a plane

Find the co-ordinates of the point A, which is at the foot of a perpendicular from the point B (1,1,9) onto a plane 2x+y-z=6. Let the vectors a and b be the points A and B.

Also note that the equation of the plane corresponds to
n.x = 6

where n = (2,1,-1) is a normal to the plane and the vector x = (x,y,z).

The vector from A to B is perpendicular to the plane so it is some multiple of n.

a = b - kn

Dotting with n and remembering that A is on the plane:

a.n = 6 = b.n - kn²

6 = -6 - 6k

k=-2

a = (5, 3, 7)