Question

Find the equations of the tangent plane and the normal line to the given surface at the specified point. The surface is defined by the equation x * y * z = 5 * eˣ * y * z. The specified point is (0, 0, 5). (a) Find the equation of the tangent plane. (b) Find the equation of the normal line (x(t), y(t), z(t)).

Answer 1

To find the equations of the tangent plane and the normal line to the given surface at the specified point (0, 0, 5), we need to first find the partial derivatives of the surface equation with respect to x, y, and z.

Step-by-step explanation:

To find the equations of the tangent plane and the normal line to the given surface at the specified point (0, 0, 5), we need to first find the partial derivatives of the surface equation with respect to x, y, and z.

Next, we substitute the coordinates of the specified point into the partial derivatives to find the gradients of the surface equation at that point. The gradient vector represents the normal vector to the tangent plane.

Using the equation of the tangent plane, we can find the equation of the normal line by parameterizing it with the coordinates of the specified point.