Consider the surface xyz = 45. How do you find the unit normal vector to the surface at the point (3, 5, 3) with positive first coordinate?

1 Answer
Jul 16, 2016

#hat n = 1/sqrt(59) ((5),(3),(5))#

Explanation:

the gradient will give you the normal vector

so for level surface #f(x,y,z) = x,y,z - 45#

#nabla f = vec n = ((yz),(xz),(xy))#

# = ((5*3),(3*3),(3*5)) = ((15),(9),(15))#

so #vec n = ((5),(3),(5))# is a normal vector

and #hat n = 1/sqrt(59) ((5),(3),(5))# is a normal unit vector