Quickie: vector normal to surface

[ilyas.h]

Homework Statement

Find vector normal to z = x^2 + y^2 - 3 at point r = (2, -1, 2)

Homework Equations

The Attempt at a Solution

here is the markscheme. I understand how to find the gradient, but i don't understand how they calculated the magnitude.

thanks

 

[Geofleur]

$z = x^2 +y^2 - 3$ is satisfied by points that form a three dimensional surface, and it's helpful to view that surface as the level surface of some function. How about viewing it as the level surface $f(x,y,z) = 0$ for $f(x,y,z) = z - x^2 - y^2 + 3$? Does that clarify things?

 

[ilyas.h]

$z = x^2 +y^2 - 3$ is satisfied by points that form a three dimensional surface, and it's helpful to view that surface as the level surface of some function. How about viewing it as the level surface $f(x,y,z) = 0$ for $f(x,y,z) = z - x^2 - y^2 + 3$? Does that clarify things?

nope. Take the magnitude of the llevel surface?

 

[SteamKing]

nope. Take the magnitude of the llevel surface?

What's the magnitude of the vector -4i + 2j + k ? This is the gradient vector at (2, -1, 2)

 

[ilyas.h]

What's the magnitude of the vector -4i + 2j + k ? This is the gradient vector at (2, -1, 2)

how does that help? i need to know how to compute the magnitude.

 

[SteamKing]

how does that help? i need to know how to compute the magnitude.

Good Lord, you're working gradient problems, but you've skipped basic vector arithmetic.

If V = ai + bj + ck, then |V| = (a² + b² + c²) ^1/2

Also |V| = (V ⋅ V)^1/2, where ⋅ signifies the dot product of two vectors.

 

[ilyas.h]

Good Lord, you're working gradient problems, but you've skipped basic vector arithmetic.

If V = ai + bj + ck, then |V| = (a² + b² + c²) ^1/2

Also |V| = (V ⋅ V)^1/2, where ⋅ signifies the dot product of two vectors.

My fault all along. I was trying to calculate the magnitude of the surface instead of the magnitude of the gradient of the surface.

Yes i know how to calculate the magnitude of a vector thank you very much.

answered.