Mavector haasi manhamba akajairwa, saka kuwanda kwakajairika hakugone kushandiswa zvakananga kwavari. Tinofanira kushandisa kuwanda kwevector. Kune mhando mbiri dzekuwanda kwevector: kuwanda kwedoti uye kuwanda kwemuchinjikwa. Kuwanda kwedoti kunonziwo scalar multiplication nekuti kunogadzira scalar quantity. Kuwanda kwemuchinjikwa kunonziwo vector multiplication nekuti kunogadzira vector quantity. Semuenzaniso, kune mavector maviri, anoti A dhani Bkuwanda kwemavectors eScalar A dhani B zvakataurwa na AB KSezvo nhandare ichishandisa madot notation, kuwanda uku kunonzi chigadzirwa chine madotsikuwanda kwevekita A dhani B zvakataurwa na A x BNekuti inoshandisa notation x, saka kuwanda uku kunonzi kuwanda kwemuchinjikwa.
Semuenzaniso, tichifunga nezve vector A dhani B sezvakaratidzwa mumufananidzo uri pazasi. Chigadzirwa chedot pakati pemavector A dhani B zvakanyorwa se AB (A poindi B).
Kutsanangura dot product yemavectors A dhani B (AB), vhekitari inoratidzwa A uye mavector Na yiyo inoumba kona θ. Tevere tinodhirowa purojekiti yevector B kuenda kunzira yevector A. Kufungidzira uku chikamu chevector B iyo yakafanana nevector A, iyo yakaenzana nehukuru hwayo B cos θ.
Saka, tinotsanangura AB sevector hombe A yakawedzerwa nezvikamu zvevector B izvo zvinoenderana ne APanyaya yemasvomhu tinogona kuinyora seinotevera:
AB cos θ inhamba yakajairika (scalar). Saka, chigadzirwa chedot chinonziwo chigadzirwa chescalar. Ko kana chigadzirwa chedot chiri pakati pemavectors A dhani B zvakadzoserwa ku BA tisati tatsanangura BA, kutanga tadhirowa purojekiti yevector A kune mavector B (ona mufananidzo uri pazasi).
Zvichibva pamufananidzo uyu, tinogona kutsanangura BA sevector hombe B yakawedzerwa nezvikamu zvevector A izvo zvinoenderana ne BPanyaya yemasvomhu tinogona kuinyora seinotevera:
Mhedzisiro yechigadzirwa cheDot AB = AB cos θ uye mhedzisiro yechigadzirwa chedot BA = BA cos θNekuti AB cos θ = BA cos θ, zvino inoshanda AB = BA
Zvimwe zvinhu zvine chekuita nekuwanda kwemadot zvaunofanira kuziva:
1. Chigadzirwa chine dot chinozadzisa mutemo wekuchinjana.
AB = BA
2. Chigadzirwa chine dot chinozadzisa mutemo wekugovera.
A. (B + C) = AB + AC
3. Kana mavector A naB akatarisana, zvinoreva kuti dot product AB = 0
Kana vhekitari A dhani B yakatarisana, ipapo kona yakagadzirwa i90o. Kos 90o = 0. Saka: AB = AB cos tit = AB kusvika 90o = 0. Kune rumwe rutivi, BA = BA cos tit = BA kusvika 90o = 0
4. Kana vhekitari A nevekitari B dziri munzira imwe chete , saka AB = AB cos 0 o = AB
Kana vhekitari A dhani B nenzira imwe chete, ipapo kona yakagadzirwa i0o. Cos 0 = 1. Saka, AB = AB cos tit = AB kusvika 0o = ABAsi zvakasiyana BA = BA cos tit = BA kusvika 0o = BA
(Haufanirwe kuvhiringidzwa ne AB dhani BAHombe AB = hombe BASemuenzaniso, hukuru hwevector A = 2. hukuru hwevector B = 3. ipapo AB = 2.3 = 6; izvi zvakafanana ne BA = 3.2 = 6.
5. Chimwe chinodiwa kuti pave nemavector maviri aenderane, kana A = B tinowana AA = A 2 kana BB = B 2
6. Kana mavector A naB ari kumativi akasiyana (kana mavector maviri ari kumativi akasiyana, kona yakagadzirwa i180º) , saka mhedzisiro yekuwanda AB = AB cos 180º = AB (-1) = -AB.
180º = -1.
Muenzaniso wematambudziko:
Vekitari A ine hukuru hwemayuniti mana uye vekitari B ine hukuru hwemayuniti matatu. Sarudza chigadzirwa chemadotsi chemavekitari maviri kana makona akaumbwa nemavekitari maviri ari 60º, 90º uye 180º.
Kukurukurirana
Sezvo AB = BA , tinogona kusarudza kushandisa chero imwe. Semuenzaniso, tinoshandisa AB
AB = AB cos theta
Saizi yeA = mayuniti mana uye saizi yeB = mayuniti matatu.
