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Wedge Product in Arbitrary Non Standard Basis

  1. Just like any other kind of Product of Vectors Wedge Product of Vectors can be calculated for Vectors given in Any Arbitrary Non Standard Basis.
  2. Following example demonstrates the calculation of the Wedge Product of Vectors A and B represented in Non Standard Basis e1, e2 and e3 as give below

    e1=[224]e2=[112]e3=[633]

    A=2e1+3e2+7e3=2[224]+3[112]+7[633]

    B=5e1+1e2+3e3=5[224]+1[112]3[633]

    A=2e1+3e2+7e3,B=5e1+1e23e3,A3=4e1+2e2+3e3

    AB=(2e1+3e2+7e3)(5e1+1e23e3)

    AB=2(e1e2)6(e1e3)15(e2e1)9(e2e3)35(e3e1)+7(e3e2))

    AB=17(e1e2)+29(e1e3)16(e2e3)

    Similarly e1e2, e1e3 and e2e3 can be calculated as follows

    e1e2=(2^e12^e2+4^e3)(1^e11^e2+2^e3)=0(^e1^e2)+0(^e1^e3)+0(^e2^e3)

    e1e3=(2^e12^e2+4^e3)(6^e13^e2+3^e3)=6(^e1^e2)18(^e1^e3)+6(^e2^e3)

    e2e3=(1^e11^e2+2^e3)(6^e13^e2+3^e3)=3(^e1^e2)9(^e1^e3)+3(^e2^e3)

    Hence AB can be given as follows

    AB=17(e1e2)+29(e1e3)16(e2e3)=17[000]+29[6186]16[393]

Related Topics
Wedge Product of Vectors,    Introduction to Vector Algebra
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