- #1
What Causes the First Plot to Be Positive and the Second Negative?
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Homework Help Overview
The discussion revolves around understanding the behavior of two plots in relation to their normal vectors and the implications of their signs. The subject area appears to involve vector calculus and geometry, particularly in the context of surfaces and planes.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the concept of normal vectors and their signs, questioning why one plot remains positive while the other becomes negative. There is an attempt to clarify the relationship between the normal vectors and the equations of the planes represented by the plots.
Discussion Status
The discussion is active, with participants questioning the terminology used (e.g., "switch") and exploring the implications of parametrization on the direction of normal vectors. Some guidance is offered regarding the use of the right-hand screw rule and the relationship between different parametrizations.
Contextual Notes
There seems to be a lack of clarity regarding the coefficients in the equations of the planes, which may be contributing to the confusion about the signs of the plots. The original poster's reference to randomness in math suggests a deeper inquiry into the underlying principles at play.
- #2
Dick
Science Advisor
Homework Helper
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If (a,b,c) is normal to a surface, so is (-a,-b,-c). There are two normals to a surface at a given point. For example in the first one you could also have written the plane -x-y-z=0. It's the same plane.
- #3
asi123
- 254
- 0
Dick said:
Yeah, but why did it switch it on the second one, and the first one stayed positive?
If I learned anything, it is that there is no random in math...
- #4
Defennder
Homework Helper
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- 4
Um, what do you mean by "switch"? I can't make out the coefficient of y in the equation of plane for the second one. You could use the right-hand screw rule along with r_u X r_v to see which direction the normal vector points. It all depends on how you parametrise it. If you had done u=y, v=x for the second one, it would have been the same as the normal vector read off the equation of the plane.
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