Question: Consider f(x,y) = ]x? + y? (a) Find the equation of a tangent plane at point (3, 4, 5). (b) Find the normal vector

Consider f(x,y) = ]x? + y? (a) Find the equation of a

Consider f(x,y) = ]x? + y? (a) Find the equation of a tangent plane at point (3, 4, 5). (b) Find the normal vector at (3, 4,5). (c) Find the parametric equations of normal lines at (3, 4, 5). (d) (i) Find the angle between the tangent plane at (3, 4, 5) and the xz -plane. (ii) Find the angle between the tangent plane at (3,4, 5) and the plane z = -x + 2y.

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