Umkhiqizo ophambene wamavekhtha amabili, isibonelo ivekhtha A dan B kubhalwe njengo A x B (A isiphambano B). Ukuphindaphinda okuphambene kubizwa ngokuthi ukuphindaphinda kwevektha ngoba umphumela walokhu kuphindaphinda ukhiqiza inani levektha.
Isibonelo, i-vector A kanye ne-vector B zibukeka njengesithombe esingezansi.
Ukuchaza umkhiqizo ohlanganisayo phakathi kwama-vector A dan B (A x B), sidweba i-vector A dan B njengoba kuboniswe esithombeni esingenhla, futhi kuboniswe izingxenye zevektha U-B uqonde ngqo ku-A, okulingana no-B sin theta.
Ngakho-ke, singachaza ubukhulu bomkhiqizo ohlanganisiwe wama-vector. A dan B (A x B) njengomkhiqizo wobukhulu be-vector A ngezingxenye zevektha B iqonde ngqo ku-vector A.
Kuthiwani uma A x B sesibuyele ekubeni khona B x A ?
Okokuqala, ake sidwebe i-vector B dan A kanye nezingxenye zevektha A okuqonde ngqo ku-B
Ngokusekelwe kulesi sibalo, singachaza umkhiqizo ohlanganisayo phakathi kwama-vector B dan A (B x A) njengomkhiqizo wobukhulu be-vector B ngezingxenye zevektha A iqonde ngqo ku-vector BKubhalwe ngokwezibalo:
Isiqondiso Sokuphindaphinda Okuphambene A x B
Umkhiqizo ophambene ungumkhiqizo we-vector, ngakho umkhiqizo unobukhulu kanye nesiqondiso. Ubukhulu bomkhiqizo we-vector buthathwe ngenhla; manje thola isiqondiso sawo. Ukuze uthole isiqondiso A x B, okokuqala sidweba amavekhtha u-A no-B njengoba kuboniswe ngezansi. Sibeka la mavekhtha amabili endaweni eyodwa.
Ukuphindaphinda okuphambene A x B ichazwa njenge-vector eqondile endizeni lapho i-vector A dan B itholakala. Usayizi uyafana no AB Isono umamkhulu. Uma C = A x B ufulawa C = AB Isono umamkhulu
U-Arah C iqonde endizeni lapho i-vector A dan B itholakala. Singasebenzisa umthetho wesandla sokunene ukuthola indlela CUma sibamba iminwe yethu ngendlela ephambene nesiqondiso sokujikeleza kwewashi, khona-ke isiqondiso C ngendlela efanayo nesithupha esibheke phezulu.
Isiqondiso Sokuphindaphinda Okuphambene B x A
Ukunquma isiqondiso B x A, okokuqala sidweba i-vector B dan A njengesithombe esingezansi. Sibeka la mavektha amabili endaweni eyodwa.
Uma C = B x A ufulawa C = I-BA sin teta.
Isiqondiso sika-C siqonde ngqo endizeni lapho i-vector ikhona khona B dan A itholakala. Singasebenzisa umthetho wesandla sokunene ukuthola indlela CUma sibamba iminwe yethu ngendlela ehambisana nendlela yokujikeleza kwezandla ngokwewashi, khona-ke indlela C kufana nendlela isithupha esikhomba ngayo phansi.
A x B akulingani no B x A. Umkhiqizo ohlanganisiwe uphumela enanini le-vector, ngaphandle kokuba nobukhulu, futhi elinokuqondisa. Kulolu hla olungenhla, isiqondiso A x B isiqondiso esiphambene ne B x A.
Ezinye izinto mayelana nokuphindaphinda okuhlanganisiwe okudingeka uzazi:
1. Ukuphindaphinda okuphambene akuvumelani nokushintshashintsha.
A x B = - B x A
Uphawu olubi lubonisa ukuthi isiqondiso B kuqhubeke A x B uhlangothi oluphambene B kuqhubeke B x A.
2. Uma amavektha amabili ehlukene i-perpendicular khona-ke i-engeli eyakhiwe ingu-90o. Ngaphandle kwama-90o = 1. Ngakho-ke, ubukhulu bomkhiqizo ophambanisayo phakathi kwama-vector A dan B kuzobukeka kanje:
A x B = AB Isono umamkhulu = AB ngaphandle 90o = AB
B x A = BA Isono umamkhulu = BA ngaphandle 90o = BA
3. Uma womabili amavektha esendleleni efanayo, khona-ke i-engeli eyakhiwe ingu-0o.
Ngaphandle kwama-0o = 0. Ngakho-ke, inani lomkhiqizo ophakathi kwama-vector A dan B kuzovela kanje.
A x B = AB Isono i-theta = AB isono 0o = 0
B x A = BA Isono i-theta = i-BA sin 0o = 0
