Find a unit normal vector to the surface x+2y+3z at the point (3,0,1) How do you normalize the gradient vector?
Follow Math Help Forum on Facebook and Google+
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 $\displaystyle \vec{n}=\frac{\vec{v}}{||\vec{v}||}=...$
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)?
Originally Posted by JJ007 $\displaystyle n=\frac{i+2j+3k}{\sqrt{14}}$ but what about at point (3,0,1)? 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.
View Tag Cloud