Multivariable Calculus | The orientation of a parametric surface with examples.

[@drpkmath12345]

Cool! Way to go! Nice explanation

[@ejacktamente]

At 6:34 he computes the cross product between r_theta and r_z to see the orientation of that particular parametrization r_1 But what if he does r_z x r_theta? The result will be exactly in the opposite direction, as the cross product is anticomutative ( a x b = - ( b x a ) ). One can say that the product should keep the order the variables has when defining the parametrization, but choosing r(theta, z) vs r(z, theta) has not particular reason, right? In a case where the surface is more complicated, I'm not going to be sure which variable goes first, nor which way the cross product should be computed.

[@Ansheshwallah]

Excellent sir ...i like your explanation. From INDIA