Ama-vector awazona izinombolo ezijwayelekile, ngakho-ke ukuphindaphinda okuvamile akukwazi ukusetshenziswa ngqo kuwo. Kumelwe sisebenzise ukuphindaphinda kwe-vector. Kunezinhlobo ezimbili zokuphindaphinda kwe-vector: ukuphindaphinda kwamachashazi kanye nokuphindaphinda okuphambene. Ukuphindaphinda kwamachashazi kubizwa nangokuthi ukuphindaphinda kwe-scalar ngoba kukhiqiza inani le-scalar. Ukuphindaphinda okuphambene kubizwa nangokuthi ukuphindaphinda kwe-vector ngoba kukhiqiza inani le-vector. Isibonelo, kunezinhlobo ezimbili ze-vector, okungukuthi A dan B. Ukuphindaphindwa kwama-vector e-Scalar A dan B kusho ukuthi AB KNjengoba inkundla isebenzisa ukubhalwa kwamachashazi, lokhu kuphindaphinda kubizwa ngokuthi umkhiqizo wamachashazi. Ukuphindaphinda kwevektha A dan B kusho ukuthi A x BNgoba isebenzisa amanothi x, khona-ke lokhu kuphindaphinda kubizwa ngokuthi ukuphindaphinda okuphambene.
Isibonelo, uma ubheka i-vector A dan B njengoba kuboniswe esithombeni esingezansi. Umkhiqizo wamachashazi phakathi kwamavektha A dan B kubhalwe njengo I-AB (A iphuzu B).
Ukuchaza umkhiqizo wamachashazi wamavektha A dan B (AB), i-vector eboniswe A kanye nama-vector Ngu-yokwakha i-engeli θ. Okulandelayo sidweba iphrojektha yevektha B ngasesiqondisweni sevektha ALokhu kuqagela kuyingxenye yevektha B okuhambisana ne-vector A, okulingana nosayizi B cos θ.
Ngakho-ke, sichaza I-AB njenge-vector enkulu A kuphindaphindwe ngezingxenye zevektha B okuhambisana ne ANgokwezibalo singakubhala kanje:
AB cos θ iyinombolo evamile (i-scalar). Ngakho-ke, umkhiqizo wechashazi ubizwa nangokuthi umkhiqizo we-scalar. Kuthiwani uma umkhiqizo wechashazi uphakathi kwama-vector A dan B kubuyiselwe emuva ku- BA ngaphambi kokuba sichaze BA, okokuqala sidweba iphrojektha yevektha A kuma-vector B (bheka isithombe ngezansi).
Ngokusekelwe kulesi sithombe, singachaza BA njenge-vector enkulu B kuphindaphindwe ngezingxenye zevektha A okuhambisana ne BNgokwezibalo singakubhala kanje:
Umphumela womkhiqizo we-Dot I-AB = AB cos θ kanye nomphumela womkhiqizo wamachashazi BA = BA cos θ. Ngoba AB cos θ = BA cos θ, bese kusebenza I-AB = BA
Ezinye izinto mayelana nokuphindaphinda kwamachashazi okudingeka uzazi:
1. Umkhiqizo wechashazi uhlangabezana nomthetho wokushintshashintsha.
I-AB = BA
2. Umkhiqizo onamachashazi uhlangabezana nomthetho wokusabalalisa.
A. (B + C) = I-AB + i-AC
3. Uma i-vector A dan B ziqonde komunye nomunye, bese kuba umphumela womkhiqizo wechashazi I-AB = 0
Lapho i-vector A dan B i-engeli eqondile komunye nomunye, khona-ke i-engeli eyakhiwe ingu-90o. I-Cos 90o = 0. Ngakho-ke: I-AB = AB cos umamkhulu = AB ibe 90o = 0. Ngakolunye uhlangothi, BA = BA cos umamkhulu = BA ibe 90o = 0
4. Uma i-vector A kanye nama-vector B indlela eyodwa,maka I-AB = AB ibe 0o = AB
Lapho i-vector A dan B ohlangothini olufanayo, khona-ke i-engeli eyakhiwe ingu-0o. Cos 0 = 1. Ngakho-ke, I-AB = AB cos umamkhulu = AB ibe 0o = AB. Ngokuphambene nalokho BA = BA cos umamkhulu = BA ibe 0o = BA
(Akufanele udideke no AB dan BA. Okukhulu AB = enkulu BAIsibonelo, ubukhulu bevektha A = 2. ubukhulu bevektha B = 3. bese kuba I-AB = 2.3 = 6; lokhu kufana nokuthi BA = 3.2 = 6.
5. Esinye isimo sokuba amavektha amabili abe sendleleni efanayo, uma A = B bese kutholakala AA = A2 noma I-BB =B2
6. Uma i-vector A dan B uhlangothi oluphambene (uma amavektha amabili ebheke ezinhlangothini eziphambene khona-ke i-engeli eyakhiwe ingu-180º), bese kuba umphumela wokuphindaphinda I-AB = AB cos 180º = AB (-1) = -AB.
I-Cos 180º = -1.
Isibonelo sezinkinga:
Ivektha A inobukhulu obungamayunithi angu-4 futhi iyi-vector B inamayunithi ama-3. Thola umkhiqizo wamachashazi wamavektha amabili uma ama-engeli akhiwe amavektha amabili angama-60º, 90º kanye no-180º.o
Ingxoxo
UKarena I-AB = BA bese singakhetha ukusebenzisa eyodwa. Isibonelo, sisebenzisa AB
I-AB = AB cos umamkhulu
Kiss A = amayunithi ama-4 kanye namakhulu B = amayunithi ama-3.
