Recent content by Flotensia

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

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

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

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?

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

I wrote by using levi-civita symbol

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

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

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?

Homework Statement Homework EquationsThe 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?

Homework Statement Homework EquationsThe 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?

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 EquationsThe Attempt at a Solution I can do nothing but just writing components of (∇u) × (∇v) · (∇w). How...

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

Homework Statement Homework EquationsThe 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?

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 EquationsThe Attempt at a Solution I could think nothing but...