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i have done a little on multivariable calculus in school -partial derivates and tangent planes to f(x,y), but now we have moved on to functions of more than 2 variables

my teacher, however, doesnt really teach us - she gives us equations and tells us to do questions and i usually find myself having to read the textbook to convince myself that i understand the equations. shes only part time so she is never about to help me at lunch time, so if you guys could help me that would be great

my textbook wasnt able to convince me why the vector grad is [tex]\nabla _{g}[/tex] is normal to the surface - surely if it has the same direction as the surface in x, y and z then it cant be going away from the surface at an angle of pi/2 rad? :S

i know that:

[tex] \nabla _{g} [/tex] = < [tex] \frac{\partial{g}}{\partial{x}} [/tex] , [tex]\frac{\partial{g}}{\partial{y}} [/tex] , [tex]\frac{\partial{g}}{\partial{z}} [/tex] >

but its not clear to me why this should be perpendicular to the surface. would you be able to help justify why it is? i dont know anything about vector spaces and stuff like that, because a level further maths is pretty limited.

any help you can provide would really be appreciated :)

my teacher, however, doesnt really teach us - she gives us equations and tells us to do questions and i usually find myself having to read the textbook to convince myself that i understand the equations. shes only part time so she is never about to help me at lunch time, so if you guys could help me that would be great

my textbook wasnt able to convince me why the vector grad is [tex]\nabla _{g}[/tex] is normal to the surface - surely if it has the same direction as the surface in x, y and z then it cant be going away from the surface at an angle of pi/2 rad? :S

i know that:

[tex] \nabla _{g} [/tex] = < [tex] \frac{\partial{g}}{\partial{x}} [/tex] , [tex]\frac{\partial{g}}{\partial{y}} [/tex] , [tex]\frac{\partial{g}}{\partial{z}} [/tex] >

but its not clear to me why this should be perpendicular to the surface. would you be able to help justify why it is? i dont know anything about vector spaces and stuff like that, because a level further maths is pretty limited.

any help you can provide would really be appreciated :)

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