Chigadzirwa chemarudzi maviri, semuenzaniso mavector A naB , chakanyorwa seA x B ( A cross B ) . Chigadzirwa chemarudzi ose chinonzi chigadzirwa chemarudzi ose nekuti mhedzisiro yekuwanda uku inoburitsa huwandu hwemavector.
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 tikashandura A x B kuita B x A?
Kutanga, tinodhirowa mavector B naA pamwe nezvikamu zvevector A zvakamira zvakananga kuna B
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 mhedzisiro yacho ine hukuru uye gwara. Hukuru hwechigadzirwa chevector hwatorwa pamusoro apa; ikozvino tinofanira kuona gwara racho. Kuti tizive gwara reA x B , tinotanga tadhirowa mavector A naB sezvakaratidzwa pazasi. Tinoisa mavector maviri aya mundege.
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
Kutungamira kwaC kwakanangana nenzvimbo ine mavector A naB . Tinogona kushandisa mutemo wekurudyi kuti tizive divi raC . Kana tikabata minwe yedu nenzira inopesana newachi, ipapo divi raC riri munzira imwecheteyo nechigunwe chakanongedzera kumusoro.
Kutungamira kweKuwanzana kweMuchinjiko B x A
Kuti tizive kwakananga B x A , tinotanga tadhirowa mavector B naA sezvakaratidzwa pazasi. Tinoisa mavector maviri aya mudenderedzwa.
Kana C = B x A Maka C = BA sin teta.
Kutungamira kwaC kwakanangana nenzvimbo iyo mavector B naA vari . Tinogona kushandisa mutemo wekurudyi kuti tizive divi raC . Kana tikabata minwe yedu nenzira yewachi, ipapo divi raC rakafanana negwara rechigunwe 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 chekuramba chinoratidza kuti divi raB paA x B rakapesana nedivi raB paB x A.
2. Kana mavector maviri aya akatarisana , kona inoumbwa i90 o . 90 o = 1. Saka, hukuru hwechigadzirwa chakapatsanurwa pakati pevectors A naB huchaonekwa seizvi:
A x B = AB sin theta = AB chivi 90 o = AB
B x A = BA sin theta = BA sin 90 o = BA
3. Kana mavector ese ari maviri ari munzira imwe chete, ipapo kona yakagadzirwa i0 o.
Chivi 0 o = 0. Saka, kukosha kwechigadzirwa chakachinjika pakati pemavector A naB kuchaonekwa seizvi.
A x B = AB sin theta = AB chivi 0 o = 0
B x A = BA sin theta = BA sin 0 o = 0
