Question

gradient of a scalar function is a vector of which of the following:-a.tangential to surface f(x,y,z)=c,b.unit normal vector to surface f(x,y,z)=c,c.normal to the surface f(x,y,z)=c​

Answer 1

Answer:

In this section we want to revisit tangent planes only this time we’ll look at them in light of the gradient vector. In the process we will also take a look at a normal line to a surface.

Let’s first recall the equation of a plane that contains the point

(x0,y0z0)

with normal vector

→n=⟨a,b,c⟩

is given by,a(x−x0)+b(y−y0)+c(z−z0)=0

Answer 2

Answer:

For a function of two variables z=f(x,y), the gradient is the two-dimensional vector <f_x(x,y),f_y(x,y)>. This definition generalizes in a natural way to functions of more than three variables.

Examples

For the function z=f(x,y)=4x^2+y^2. The gradient is

displaymath64

For the function w=g(x,y,z)=exp(xyz)+sin(xy), the gradient is

displaymath66