Chigadzirwa chemuchinjikwa chevectors mbiri, semuenzaniso vector A dhani B zvakanyorwa se A x B (A silang B). Kuwanda kwemuchinjikwa kunonzi kuwanda kwevector nekuti mhedzisiro yekuwanda uku inoburitsa huwandu hwevector.
Semuenzaniso, vector A nevector B zvinotaridzika semufananidzo uri pazasi.
Kutsanangura chigadzirwa chakasiyana pakati pemavector A dhani B (A x B), tinodhirowa vhekitori A dhani B sezvakaratidzwa mumufananidzo uri pamusoro, uye zvakare zvakaratidzwa zvikamu zvevector B yakatarisana naA, iyo yakaenzana naB sin theta.
Saka, tinogona kutsanangura hukuru hwechigadzirwa chemuchinjikwa chemavectors. A dhani B (A x B) sechibereko chehukuru hwevector A nezvikamu zvevector B yakatarisana nevector A.
Ko kana A x B tadzokera pakuvapo B x A ?
Kutanga, ngatidhirowei vhekita B dhani A uye zvikamu zvevector A iyo yakatarisana neB
Zvichibva pamufananidzo uyu, tinogona kutsanangura chigadzirwa chakasanganiswa pakati pemavector B dhani A (B x A) sechibereko chehukuru hwevector B nezvikamu zvevector A yakatarisana nevector BYakanyorwa nemasvomhu:
Kutungamira kweKuwanzana kweMuchinjiko A x B
Chigadzirwa chakachinjika chigadzirwa chevector, saka chigadzirwa chine hukuru uye gwara. Hukuru hwechigadzirwa chevector hwatorwa pamusoro apa; ikozvino sarudza gwara racho. Kuti uone gwara A x B, kutanga tinodhirowa mavector A naB sezvakaratidzwa pazasi. Tinoisa mavector maviri aya mudenderedzwa.
kuwanda kwemuchinjikwa A x B inotsanangurwa sevector yakatarisana nendege umo vector A dhani B iripo. Saizi yacho yakafanana neye AB chivi tit. Kana C = A x B Maka C = AB chivi tit
Ara C yakatarisana nendege umo vhekita A dhani B iri. Tinogona kushandisa mutemo weruoko rwerudyi kuti tizive kwainoenda CKana tikabata minwe yedu nenzira yakatarisana nekwaitenderera newachi, ipapo nzira yacho ndiyo C nenzira imwecheteyo nechigunwe chakanongedzera kumusoro.
Kutungamira kweKuwanzana kweMuchinjiko B x A
Kuti uzive gwara B x A, kutanga tadhirowa vhekitari B dhani A semufananidzo uri pazasi. Tinoisa mavector maviri aya mudenderedzwa.
Kana C = B x A Maka C = BA sin teta.
Kutungamira kwaC kwakatarisana nendege uko vhekita iri B dhani A iri. Tinogona kushandisa mutemo weruoko rwerudyi kuti tizive kwainoenda CKana tikabata minwe yedu nenzira inoenderana nekwaitenderera maoko tichitenderera newachi, ipapo nzira yacho ndiyo C zvakafanana nekwakananga chigunwe chakanongedzera pasi.
A x B hazvina kuenzana ne B x AChigadzirwa chakasanganiswa chinoguma nehuwandu hwevector, iyo kunze kwekuva nehukuru, ine gwara zvakare. Mudonhwe riri pamusoro apa, gwara A x B nzira yakatarisana ne B x A.
Zvimwe zvinhu zvine chekuita nekuwanda kwehuwandu hwezvinhu zvaunofanira kuziva:
1. Kuwanda kwezvikamu zvakasiyana-siyana hakubvumiri kuchinja.
A x B = - B x A
Chiratidzo chisina kunaka chinoratidza kuti gwara B pada A x B divi rakapesana B pada B x A.
2. Kana mavector maviri aya akasiyana yakatwasuka ipapo kona yakagadzirwa i90o. Pasina makumi matatu nemavirio = 1. Saka, hukuru hwechigadzirwa chakachinjika pakati pemavector A dhani B zvichataridzika seizvi:
A x B = AB chivi tit = AB pasina 90o = AB
B x A = BA chivi tit = BA pasina 90o = BA
3. Kana mavector ese ari maviri ari munzira imwe chete, kona yakagadzirwa i0o.
Pasina makumi matatu nemavirio = 0. Saka, kukosha kwechigadzirwa chakachinjika pakati pemavector A dhani B zvichaonekwa seizvi.
A x B = AB chivi theta = AB chivi 0o = 0
B x A = BA chivi theta = BA chivi 0o = 0
