๏ผvar๏ผlogmarcus chiu

Trivectors - 3-Vectors

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Trivectors - 3-Vectors
  • is a k-vector where k=3
  • When we take the wedge product of 3 vectors result is, ๐ฎโˆง๐ฏโˆง๐ฐ = (๐‘ข1๐‘ฃ2๐‘ค3+ ๐‘ข2๐‘ฃ3๐‘ค1 + ๐‘ข3๐‘ฃ1๐‘ค2โˆ’ ๐‘ข1๐‘ฃ3๐‘ค2 โˆ’ ๐‘ข2๐‘ฃ1๐‘ค3 โˆ’ ๐‘ข3๐‘ฃ2๐‘ค1)(๐ž1โˆง๐ž2โˆง๐ž3)
    • scalar part is the volume of the parallelepiped (i.e. ๐‘ข1๐‘ฃ2๐‘ค3+ ๐‘ข2๐‘ฃ3๐‘ค1 + ๐‘ข3๐‘ฃ1๐‘ค2โˆ’ ๐‘ข1๐‘ฃ3๐‘ค2 โˆ’ ๐‘ข2๐‘ฃ1๐‘ค3 โˆ’ ๐‘ข3๐‘ฃ2๐‘ค)
    • trivector part is the โ€œdirectionโ€ of that volume (i.e. ๐ž1โˆง๐ž2โˆง๐ž3)