A normal to the given plane is i + 2j + 3k.
A normal to the paraboloid is .
A normal of the tangent plane at the point (a, a^2 + b^2, b) is therefore (2a) i - j + (2b) k.
You want to find the point at which the tangent plane has a normal parallel to i + 2j + 3k. You therefore want the values of a and b such that where is a scalar. So solve the following equations simultaneously:
... (1)
... (2)
... (3)