Maveketa si manambala wamba, kotero kuchulukitsa wamba sikungagwiritsidwe ntchito mwachindunji kwa iwo. Tiyenera kugwiritsa ntchito kuchulukitsa kwa vekita. Pali mitundu iwiri ya kuchulukitsa kwa vekita: kuchulukitsa kwa dot ndi kuchulukitsa kodutsana. Kuchulukitsa kwa dot kumatchedwanso kuchulukitsa kwa scalar chifukwa kumapanga kuchuluka kwa scalar. Kuchulukitsa kodutsana kumatchedwanso kuchulukitsa kwa vekita chifukwa kumapanga kuchuluka kwa vekita. Mwachitsanzo, pali maveketa awiri, omwe ndi A dani BKuchulukitsa kwa ma vectors a scalar A dani B adanenedwa ndi AB KPopeza bwaloli limagwiritsa ntchito madontho, kuchulukitsa kumeneku kumatchedwa chinthu cha dontho. Kuchulukitsa kwa vekitala A dani B adanenedwa ndi A x BChifukwa imagwiritsa ntchito zolemba x, ndiye kuchulukitsa kumeneku kumatchedwa kuchulukitsa kodutsana.
Mwachitsanzo, poganizira za vekitala A dani B monga momwe chithunzi chili pansipa chikusonyezera. Chopangidwa ndi dontho pakati pa ma vector A dani B yolembedwa ngati AB (A mfundo B).
Kufotokozera zotsatira za dot za ma vector A dani B (AB), vekitala yojambulidwa A ndi ma vector Ndi yzomwe zimapanga ngodya θ. Kenako tijambula chiwonetsero cha vekitala B kulowera komwe vekitala ikupita AChiwonetserochi ndi gawo la vekitala B zomwe zili zofanana ndi vector A, yomwe ndi kukula kofanana ndi B cos θ.
Motero, timafotokoza AB ngati vekitala wamkulu A kuchulukitsidwa ndi zigawo za vekitala B zomwe zikufanana ndi AMwa masamu tingathe kulemba motere:
AB cos θ ndi nambala wamba (scalar). Chifukwa chake, chinthu cha dot chimatchedwanso chinthu cha scalar. Nanga bwanji ngati chinthu cha dot pakati pa ma vector A dani B kusinthidwa kukhala BA tisanafotokoze BAChoyamba, timajambula chithunzi cha vekitala A kwa ma vector B (onani chithunzi pansipa).
Kutengera ndi chithunzichi, titha kufotokoza BA ngati vekitala wamkulu B kuchulukitsidwa ndi zigawo za vekitala A zomwe zikufanana ndi BMwa masamu tingathe kulemba motere:
Zotsatira za chinthu cha dot AB = AB cos θ ndi zotsatira za chinthu cha dot BA = BA cos θ. Chifukwa AB cos θ = BA cos θ, kenako imagwira ntchito AB = BA
Zinthu zina zokhudza kuchulukitsa madontho zomwe muyenera kudziwa:
1. Chogulitsa cha dot chimakwaniritsa lamulo loyendetsera zinthu.
AB = BA
2. Chogulitsa cha dot chimakwaniritsa lamulo logawa.
A. (B + C) = AB + AC
3. Ngati vekitala A dani B mopingasa kwa wina ndi mnzake, kenako zotsatira za chinthu cha dontho AB = 0
Pamene vekitala A dani B mopingasa kwa wina ndi mnzake, ndiye kuti ngodya yopangidwa ndi 90o. Cos 90o = 0. Motero: AB = AB cos titi = AB 90o = 0. Kumbali inayi, BA = BA cos titi = BA 90o = 0
4. Ngati vekitala A ndi ma vector B Mbali Imodzi,maka AB = AB 0o = AB
Pamene vekitala A dani B mbali yomweyo, ndiye kuti ngodya yopangidwa ndi 0o. Cos 0 = 1. Chifukwa chake, AB = AB cos titi = AB 0o = AB. M'malo mwake BA = BA cos titi = BA 0o = BA
(Simuyenera kusokonezedwa ndi AB dani BAChachikulu AB = chachikulu BAMwachitsanzo, kukula kwa vektara A = 2. kukula kwa vekitala B = 3. kenako AB = 2.3 = 6; izi ndi zofanana ndi BA = 3.2 = 6.
5. Chinthu china choti ma vector awiri akhale mbali imodzi, ngati A = B kenako analandira AA = A2 kapena BB =B2
6. Ngati vekitala A dani B mbali yosiyana (pamene ma vector awiri ali mbali zosiyana ndiye kuti ngodya yopangidwa ndi 180º), kenako zotsatira za kuchulukitsa AB = AB cos 180º = AB (-1) = -AB.
Cos 180º = -1.
Chitsanzo cha mavuto:
Vekitala A ili ndi kukula kwa mayunitsi 4 ndipo ndi vector B Ili ndi mayunitsi atatu. Dziwani zotsatira za dot ya mavekitala awiriwa ngati ma angles opangidwa ndi mavekitala awiriwa ndi 60º, 90º ndi 180º.o
Zokambirana
Chifukwa AB = BA kenako tingasankhe kugwiritsa ntchito imodzi. Mwachitsanzo, timagwiritsa ntchito AB
AB = AB cos titi
Kupsompsona A = mayunitsi 4 ndi akuluakulu B = mayunitsi atatu.
