reciprocal vectors, Prob54

Discussion in 'Math' started by PG1995, Apr 15, 2012.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi

    Please have a look on the attachment and kindly help me with queries there. I'm sorry if answer to any of the queries is obvious. Right now, I'm very much exhausted and time-constrained. Thank you.

    Regards
    PG
     
  2. panic mode

    Senior Member

    Oct 10, 2011
    1,318
    304
    Q2: this is basic algebra:

    start from
    B(A*CxD) - A(B*CxD) = C(A*BxD) - D(A*BxC)

    move the last term to the left (changes sign):
    D(A*BxC) + B(A*CxD) - A(B*CxD) = C(A*BxD)

    move second and third term to the right (they both change sign):
    D(A*BxC) = -B(A*CxD) + A(B*CxD) + C(A*BxD)

    reorder second and third term:
    D(A*BxC) = A(B*CxD) - B(A*CxD) + C(A*BxD)

    finally divide everything by bracket on the left in order to free D:
    D(A*BxC)/(A*BxC) = [A(B*CxD) - B(A*CxD) + C(A*BxD)]/(A*BxC)

    note (A*BxC)/(A*BxC) = 1

    so we get

    D*1 = [A(B*CxD) - B(A*CxD) + C(A*BxD)]/(A*BxC)
    or
    D= A(B*CxD)/(A*BxC) - B(A*CxD)/(A*BxC) + C(A*BxD)/(A*BxC)
     
  3. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Thank you, panic mode, and sorry I have been little late with my thanks. Actually I was very much busy till yesterday.

    Regards
    PG
     
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