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  1. F

    Normal vector of curved surface

    I was so silly. It helps me a lot. Thanks for your help!!
  2. F

    Normal vector of curved surface

    I can explain that in word and can image in mind, but i can't in numerical expression... That's my problem...
  3. F

    Relationship between electric potential and electric field

    Don't we have to show the quantity of point is scalar or vector??
  4. F

    How to prove some functions are scalar field or vector field

    Text says scalar is invariant in rotational transformation.Then to prove some functions are scalar field, should I do rotational transformation, or are there any other methods?
  5. F

    Relationship between electric potential and electric field

    Scalar field means the function of points associating scalar value. Is it clear?Then should I do rotational transformation to prove?
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    Identity by using gradient

    I wrote by using levi-civita symbol
  7. F

    Normal vector of curved surface

    Ahh, I got what 2 parameters mean. Thanks. then could you help me more to solve that problem??
  8. F

    Identity by using gradient

    Scalar triple product means det(a,b,c) or volume of a parallelepiped. Is it a key to solve this problem?
  9. F

    Normal vector of curved surface

    I'm so sorry. It was my first time to write in this forum. I know that cross product makes perpendicular vectors. But in this problem, I don't understand how we explain three dimension by using two parameter, u and v. I searched in internet and thought it is related to gradient. Is it right?
  10. F

    Angular momentum in gravitational field

    Homework Statement Homework Equations The Attempt at a Solution I can't understand what is ɛ in this problem, and why should we adopt it. Could you explain me please?
  11. F

    How to prove some functions are scalar field or vector field

    Homework Statement Homework Equations The Attempt at a Solution I solved #2,4 but I don't understand what #1,3 need to me. I know that scalar field is a function of points associating scalar value. But how can I prove some function is scalar field or vector field?
  12. F

    Identity by using gradient

    Homework Statement Let us consider three scalar fields u(x), v(x), and w(x). Show that they have a relationship such that f(u, v, w) = 0 if and only if (∇u) × (∇v) · (∇w) = 0. Homework Equations The Attempt at a Solution I can do nothing but just writing components of (∇u) × (∇v) · (∇w)...
  13. F

    Normal vector of curved surface

    Homework Statement Homework Equations The Attempt at a Solution I can understand it intuitively, but can't prove mathematically...Can you help me??
  14. F

    Relationship between electric potential and electric field

    Homework Statement Homework Equations The Attempt at a Solution I could find how to solve #2,4, but I don't understand what #1,3 need to me. How can I prove some functions are scalar field or vector field?
  15. F

    Identity by using gradient

    Homework Statement Let us consider three scalar fields u(x), v(x), and w(x). Show that they have a relationship such that f(u, v, w) = 0 if and only if (∇u) × (∇v) · (∇w) = 0. Homework Equations The Attempt at a Solution I could think nothing...
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