At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 3x + 2y + 7z = 2? (if an answer does not exist, enter dne.) (x, y, z) =

If represent a family of surfaces for different values of the constant . The gradient of the function defined as is a vector normal to the surface .

Given the paraboloid

.

We can rewrite it as a scalar value function f as follows:



The normal to the paraboloid at any point is given by:



Also, the normal to the given plane is given by:



Equating the two normal vectors, we have:



Since, -1 = 2 is not possible, therefore there exist no such point on the paraboloid such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2.