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.
AB = BA
2. Umkhiqizo onamachashazi uhlangabezana nomthetho wokusabalalisa.
A. (B + C) = AB + AC
3. Uma amavekhtha u-A no- B eqondene, khona-ke umkhiqizo wechashazi u-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 ne-vector B zisehlangothini olufanayo , khona-ke u-AB = AB cos 0 o = 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 samavektha amabili ohlangothini olufanayo, uma u-A = B khona-ke sithola u-AA = A 2 noma u-BB = B 2
6. Uma amavekhtha u-A no -B ebhekene ngezindlela eziphambene (lapho amavekhtha amabili ebhekene ngezindlela eziphambene, i-engeli eyakhiwe ingu-180º) , khona-ke umphumela wokuphindaphinda u-AB = AB cos 180º = AB (-1) = -AB.
I-Cos 180º = -1.
Isibonelo sezinkinga:
Ivektha u- A inobukhulu obungamayunithi ama-4 kanti ivektha u -B inobukhulu obungamayunithi ama-3. Nquma umkhiqizo wamachashazi wamavektha amabili uma ama-engeli akhiwe yivektha amabili angama-60º, 90º kanye no-180º.
Ingxoxo
Njengoba u-AB = BA , singakhetha ukusebenzisa noma yikuphi. Isibonelo, sisebenzisa u-AB
AB = AB cos theta
Usayizi wamayunithi angu -A = 4 kanye nosayizi wamayunithi angu -B = 3.
