How do you find the equation of the normal vector in relation to flux using a general method? If possible, explain it for the x,y; theta,z; and phi, theta parametrizations.

Question

anonymous · Answer

first you have to parametrize the surface with 2 variables
and then you get the normal vector by doing the x product of the derivatives of each one of them
for example
x=2 cos t
y=2 sin t
z= z       0<z<10-x-y

i                               j                             k
-2sin t=(dx/dt)       2 cos t=(dy/dt)          0=(dz/dt)
0=(dx/dz)                0=(dy/dz)               1=(dz/dz)

and your normal vector to that surface would be (2cos t ;  2sin t ; 0)