Check that the point (0, 1, 3) lies on the given surface. Then, viewing the surface as a level surface for a function f(x, y, z), find a vector normal to the surface at (0, 1, 3). y = 9/(2x + 3z)

Therefore (0,1,3) lies on the given surface.

Therefore a vector normal to the surface at (0,1,3) is

Step-by-step explanation:

Given equation of the surface is

First we arrange the equation of the surface in the form of f(x,y,z) =0.

Therefore

If the point (0,1,3) lies on the given surface. Then it will be satisfy the equation.

putting x=0, y= 1 and z=3

f(0,1,3) = 1(2.0+3.3)-9 = 9-9=0

Therefore (0,1,3) lies on the given surface.

In order to find the normal at any point in vector space we use the gradient operator:

Here,            

The normal vector of the surface at (0,1,3) is

Therefore a vector normal to the surface at (0,1,3) is

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540