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# Orientation and stokes

Determining the proper orientation of a boundary given the orientation of the normal vector. Created by Sal Khan.

## Want to join the conversation?

• Why is Sal drawing 3D bodies? I thought Stokes theorem deals with 2D surfaces in 3D space.
• You are correct in that it applies to surfaces in 3D. However, Sal isn't drawing "volumes." He is simply sketching a surface (in purple) and its boundary (in blue). It sort of looks like a 3D body, but it's not filled in.
• for the end of the video, I've learned in physics and in a course of mechanics whats called the rule of the right hand (or whatever it's called in english) for the momentum . anyway, your thumb is the direction of the normal vector and the four fingers (when you twist your wrist) show the way you "walk" to. can i apply this rule here or is it just a coincidence that the two rules match?
• Yes, you can apply the rule here. Counterclockwise direction is usually considered to be positive.
• Can we not just use the right hand rule?
• A lot of people have been asking this question. Yes, you can just use the right-hand rule. I strongly prefer it, for it is very intuitive.
• Am I becoming delirious from studying for my final or is this little man really walking the wrong way on this video to be keeping the surface to his left?
• Try your keyboard and a pencil. First walk along with your pencil around your keyboard(the side with your keys) with the keyboard on the left of your pencil (make sure you know what you define as the left side of your pencil). Now take the backside of your keyboard ( the side with no keys and do the same). Counterclockwise in the first case, it becomes clockwise in the second.

Visualizing it is cumbersome, so I just use the right hand rule. :)
• Can't we use the right-hand rule? It seems it works perfectly.
• plz tell me about volume integrals ....to find volume integrals,..
(1 vote)
• A volume integral is simply a triple integral. For example, think of some mass density, p, which is a function of x, y and z - let p = xyz.
Now, say you want to find the total amount of mass in a cubic region bounded by the origin, and a point at (2,4,6). You can draw this as a cuboid in the xyz plane.
You can set up a volume integral of p with respect to x, y and z, with 3 limits for x (0 to 2), y (0 to 4) and z (0 to 6).
Now, you solve the integral in any order - for simplicity integrate with respect to (wrt) x first (ie. (x^2)/2), then you can factor out that x term leaving only yz inside the integral - you can calculate the limits of the x term outside of the integral. Then solve for y, factor out, and finally solve for z.

If you'd like to give the above example a try, let p = 5xyz, and use the same cuboid (0,0,0) to (2,4,6), and you should find that the volume integral solves to 1440kg.
• The little guy's head should point to the normal of where he is. The first example, where the normal is pointing up, by the time the point moves to where the little guy is, it should be twisted to pointing outside, i.e. downward. Same for the second example, the normal is pointing inside.
The bottle cap example, are we twisting the bottle or the cap? If we hold the cap stationary and twist the bottle instead, we get the other result. After applying the right-hand rule, we come to the conclusion that the bottle stays and cap turns.
Thanks for the video!
(1 vote)
• there is also the right hand trick:
if you imagine that you grab the surface with your four fingers oriented in the direction of the rotation, your thumb indicate the normal vector orientation! ;P
(1 vote)
• Enjoyed the bottle analogy. Lefty loosy righty tighty
(1 vote)
• How does orientation relate to physics ?
(1 vote)