(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the unit vector with positivezcomponent which is normal to the surface z = x^2*y + x*y^4 at the point (1,1,2) on the surface

3. The attempt at a solution

So I find:

dz/dx = 2xy +y^4

dz/dy = x^2 + 4xy^3

Substitute (1,1) in those equations and get dz/dx = 3, and dz/dy = 5

So now we have (3, 5, -1)

Multiply by -1 and now we have (-3, -5, 1), but it's apparently wrong.

However the answer was (-3/35*sqrt(35), -1/7*sqrt(35), 1/35*sqrt(35))

I haven't the faintest idea as to how that came about, well...it seems to have been multiplied by sqrt(35)/35, except for the second component which appears to have something else done to it.

I looked around for how the normal vector is calculated in my book, and online too; it's pretty much what I've done.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Calculating the normal vector to a surface

**Physics Forums | Science Articles, Homework Help, Discussion**