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How to prove vector identities WITHOUT using levi civita ?

  1. Nov 27, 2017 #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.)
    Last edited by a moderator: Nov 27, 2017
  2. jcsd
  3. Nov 27, 2017 #2


    Staff: Mentor

  4. Nov 27, 2017 #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.
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