Question

F=X2+y2-z=1
Fine the unit vector is normal to this surface at P(1,1,1)

Answer 1

Given surface is-

$$f(x,y,z)=x^2+y^2-z=1$$

So,

The normal at point (1,1,1) will be-

Direction ratios of normal will be-

$$(\frac{1}{1},\frac{1}{1},\frac{1}{1})$$

$$Or\\(1,1,1)$$

Unit normal vector =

$$\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{k}$$