Hello sir, how do we get to know that ru ×rv will give the outward normal vector or rv×ru will give the normal vector as the choice of u and v depends on us i.e. for eg. someone can put x=u, y=v and someone other can take x=v, y=u
U is the angle with respect to z axis. Since the surface is upper hemisphere so z is positive and hence 0 to pi/2. If possible, see my lecture on spherical coordinates..
Thank you Sir. You really saved my M3.
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I have been struggling with vector calculus a lot and you have been of great help. Thank you
Glad to hear that..all the best 😊
Wonderful teaching sir
Thank you 😊
Hello sir, how do we get to know that ru ×rv will give the outward normal vector or rv×ru will give the normal vector as the choice of u and v depends on us i.e. for eg. someone can put x=u, y=v and someone other can take x=v, y=u
U r right. If you take x=v and y=u then normal vector will be downward( inward).
It depends on what parameterization u r taking.
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Okay sir thank you
@@aviraj983 welcome
Sir how do you know that a specific shape is parallel to xy plane and how did you take the limits of u for the for the 2nd question for S2 surface
S2 is a disc of radius 1. So u will be from 0 to 1.
Timestamp for first question?
Sir, In the hemisphere problem 'u' should be 0 to pi? If I am wrong, how did it came 0 to pi/2
U is the angle with respect to z axis. Since the surface is upper hemisphere so z is positive and hence 0 to pi/2. If possible, see my lecture on spherical coordinates..
At 10:27 how did r(u,v) came? i did not understand please explain
These are spherical coordinates::
th-cam.com/video/WI5Iyx2ne-I/w-d-xo.html
At 16:15 how did the limits of x and y came?
Given that |x|