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foo9008
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Can you give some example?BvU said:Try a few examples and you'll see.
Remember when vectors are perpendicular
and when lines are perpendicular
i still don't understand what do you mean, can you explain further?BvU said:z = x
why it will become like this ?vela said:The surface ##\sigma## is defined by ##\phi(x,y,z)=0## where ##\phi(x,y,z)=z-f(x,y)##, and the normal is the gradient of ##\phi(x,y,z)##. What do you get when you calculate that?
I'm sure this is covered in your textbook.foo9008 said:why it will become like this ?
A normal vector is a vector that is perpendicular to a surface at a given point. It is used to determine the orientation and direction of the surface for the purposes of calculating a surface integral of a vector field.
There are multiple methods for calculating a normal vector, depending on the specific surface and vector field being considered. In general, the normal vector can be found by taking the cross product of two tangent vectors to the surface at a given point.
A normal vector is important because it determines the direction and orientation of the surface being integrated over. This is necessary for accurately calculating the flux or flow of a vector field over the surface.
Yes, a normal vector can have a negative magnitude. This indicates that the surface is oriented in the opposite direction to the chosen direction of the normal vector. However, in most cases, the magnitude of the normal vector is not as important as its direction.
The normal vector is used to determine the orientation and direction of the surface, which is necessary for setting up the integral. It is also used to calculate the dot product with the vector field, which is a key step in evaluating the surface integral.