Umkhiqizo ohlanganisiwe wamavektha amabili, isibonelo amavektha u-A no -B, ubhalwa njengo- A x B ( A ohlanganisiwe u -B ). Umkhiqizo ohlanganisiwe ubizwa ngokuthi umkhiqizo wevektha ngoba umphumela walokhu kuphindaphindwa 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 siguqula u-A x B sibe u-B x A?
Okokuqala, sidweba amavekhtha u-B no -A kanye nezingxenye zevekhtha u -A eziqondene no-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-ke umphumela unamandla kanye nesiqondiso. Ubukhulu bomkhiqizo we-vector buthathwe ngenhla; manje sidinga ukunquma isiqondiso sawo. Ukuze sinqume isiqondiso se- A x B , siqala ngokudweba ama-vector u-A no-B njengoba kuboniswe ngezansi. Sibeka la ma-vector amabili endizeni.
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
Isiqondiso sika- C siqonde ngqo endaweni lapho amavektha u-A no -B elele khona. Singasebenzisa umthetho wesandla sokudla ukuthola isiqondiso sika- C. Uma sibamba iminwe yethu ngendlela ephikisana newashi, khona-ke isiqondiso sika- C sisehlangothini olufanayo nesithupha esibheke phezulu.
Isiqondiso Sokuphindaphinda Okuphambene B x A
Ukuze sithole indlela u-B x A , siqala ngokudweba amavektha u-B no -A njengoba kuboniswe ngezansi. Sibeka la mavektha amabili endizeni.
Uma C = B x A ufulawa C = I-BA sin teta.
Isiqondiso sika-C siqonde ngqo endaweni lapho amavektha u-B no -A elele khona. Singasebenzisa umthetho wesandla sokudla ukuthola isiqondiso sika- C. Uma sibamba iminwe yethu ngendlela yewashi, khona-ke isiqondiso sika- C sifana nesiqondiso sesithupha esikhomba 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 olunegethivu lubonisa ukuthi isiqondiso sika -B ku- A x B siphambene nesiqondiso sika -B ku - B x A.
2. Uma amavekhtha amabili eqonde komunye nomunye , i-engeli eyakhiwe ingu-90 o . Isono 90 o = 1. Ngakho-ke, ubukhulu bomkhiqizo ophambanisayo phakathi kwamavekhtha u-A no -B buzovela kanje:
A x B = AB sin theta = AB isono 90 o = AB
B x A = BA sin theta = BA sin 90 o = BA
3. Uma womabili amavektha esendleleni efanayo, khona-ke i-engeli eyakhiwe ingu-0 o.
Isono 0 o = 0. Ngakho-ke, inani lomkhiqizo ophambanisayo phakathi kwamavekhtha u-A no -B lizovela kanje.
A x B = AB sin theta = AB isono 0 o = 0
B x A = BA sin theta = BA sin 0 o = 0
