How to prove vector identities WITHOUT using levi civita ?

In summary, the conversation discusses deriving vector identities in electromagnetic theory books and ways to improve the ability to solve them quickly. The individual mentions a method they noticed, using lectures and notes as resources, and the preference for component-based proofs. They also mention the need to finish half of the book in a short amount of time for an upcoming exam.
  • #1
darksilence
6
1
Mentor note: Thread moved from homework sections as being a better fit in the math technical section.
Multiplying components of both sides are also off limits.
I am trying to derive vector identities on introduction chapters in various EMT books. For example : (AXB).(CXD) = (A.C)(B.D) - (A.D)(B.C)
After a few hours i noticed B.(CXD) = C.(DXB) and replaced B's with AXB's its Done.
AX(BX(CXD)) was even simpler didnt take any time at all.
I want to do that to
∇. (AXB) = B.(∇xA) - A.(∇xB)
∇x(AxB) = ...
∇(A.B) = ...
∇x(∇xA) = ∇(∇.A) - ∇2A etc

So far last 2 days after solving the first two of them just looking them and hoping to see it. What i should do to improve my ability to see them fast ? (I also have to finish half the book in 2-3 weeks before exam so i am hoping to solve this problem in a few days at most.)
 
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  • #3
Thank you. It wasnt what i wanted at all but some way i didnt imagine they were still helpfull. Instead of working on my weakness i will go on with my strengths.
 

1. How can I prove vector identities without using the Levi-Civita symbol?

There are various methods for proving vector identities without using the Levi-Civita symbol. These include using vector calculus, algebraic manipulations, and direct geometric proofs.

2. Can I use other mathematical concepts to prove vector identities instead of the Levi-Civita symbol?

Yes, you can use other mathematical concepts such as dot and cross products, vector projections, and the properties of vector operations to prove vector identities without using the Levi-Civita symbol.

3. Is it necessary to use the Levi-Civita symbol to prove all vector identities?

No, the Levi-Civita symbol is not essential for proving all vector identities. Some identities can be proven using other methods, while others may require the use of the Levi-Civita symbol.

4. Are there any advantages to proving vector identities without using the Levi-Civita symbol?

Yes, proving vector identities without using the Levi-Civita symbol can often provide a deeper understanding of the underlying mathematical concepts and principles. It also allows for more flexibility and creativity in problem-solving.

5. What are some resources for learning how to prove vector identities without using the Levi-Civita symbol?

There are many online resources and textbooks available that provide detailed explanations and examples of how to prove vector identities without using the Levi-Civita symbol. You can also consult with a mathematics tutor or attend workshops or seminars on the topic.

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