Give a general formula for parametric equations for the normal line to a surface given by the equation
F(x, y, z) = 0 at the point (x0, y0, z0) on the surface. (See Exercise 34.)
34. This problem concerns the surface defined by the equation
x 3 z + x2 y2 + sin (yz) = −3.
(a) Find an equation for the plane tangent to this surface at the point (−1, 0, 3).
(b) The normal line to a surface S in R3 at a point (x0, y0, z0) on it is the line that passes through (x0, y0, z0) and is perpendicular to S. Find a set of parametric equations for the line normal to the surface given above at the point (−1, 0, 3).
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