# Unit normal vectors

• Jun 7th 2010, 02:52 PM
JJ007
Unit normal vectors
Find a unit normal vector to the surface x+2y+3z at the point (3,0,1)

How do you normalize the gradient vector?
• Jun 7th 2010, 02:57 PM
TheEmptySet
Quote:

Originally Posted by JJ007
Find a unit normal vector to the surface x+2y+3z at the point (3,0,1)

How do you normalize the gradient vector?

To normalize ANY vector divide it by its magnitude

So the normal vector is $\displaystyle \vec{v}=\vec{i}+2\vec{j}+3\vec{k}$

Then the unit normal is $\displaystyle \vec{n}=\frac{\vec{v}}{||\vec{v}||}=...$
• Jun 7th 2010, 03:09 PM
JJ007
Quote:

Originally Posted by TheEmptySet
To normalize ANY vector divide it by its magnitude

So the normal vector is $\displaystyle \vec{v}=\vec{i}+2\vec{j}+3\vec{k}$

Then the unit normal is $\displaystyle \vec{n}=\frac{\vec{v}}{||\vec{v}||}=...$

$\displaystyle n=\frac{i+2j+3k}{\sqrt{14}}$ but what about at point (3,0,1)?
• Jun 7th 2010, 03:15 PM
TheEmptySet
Quote:

Originally Posted by JJ007
$\displaystyle n=\frac{i+2j+3k}{\sqrt{14}}$ but what about at point (3,0,1)?

Quote:

Find a unit normal vector to the surface x+2y+3z at the point (3,0,1)
If I understand this correctly you have an equation of a plane

$\displaystyle x+22y+3z=?$

If that is correct planes have the same gradient at every point.