Hey y'all, this is my first post. I am currently stuck on a multivariable question. Please let me know if you can help. 1. The problem statement, all variables and given/known data The point, P = (1, 2, 2) lies on the surface z = x^2 + y^2 -3x. Find parametric equations for the tangent line to the surface through the point P parallel to the plane x = 1. 2. Relevant equations Gradient vector ∇F(x,y) = < dF/dx, dF/dy> Normal vector n = < dF/dx, dF/dy, -1> General form of tangent vector: dF/dx(x-x0) + dF/dy(y-y0) + dF/dz(z-z0) 3. The attempt at a solution ∇F(x,y) = < 2x -3, 2y > n = < 2x-3, 2y, -1> n(1, 2, 2) = < -1, 4, -1> -1(x-1) + 4(y-2) -1(z-2) = 0 -x + 1 +4y - 8 -z + 2 = 0 -x + 4y -z = 5 This is where I am stuck. In order to be parallel to the plane x=1, should the parametric equations be x = 1, y = 2 + 4t, z = 2 - t or would it still be the tangent equation x = 1 - t, y = 2 + 4t, z = 2-t?