Samfurin giciye na vectors guda biyu, misali vector A dan B an rubuta kamar A x B (A silang B). Ana kiran ninkawar giciye ninkawar vector saboda sakamakon wannan ninkawar yana samar da adadin vector.
Misali, vector A da vector B suna kama da hoton da ke ƙasa.
Don ayyana samfurin giciye tsakanin vectors A dan B (A x B), muna zana vector A dan B kamar yadda aka nuna a hoton da ke sama, kuma an nuna kayan aikin vector B yana daidai da A, wanda yayi daidai da B sin theta.
Saboda haka, za mu iya ayyana girman samfurin giciye na vectors. A dan B (A x B) a matsayin samfurin girman vector A tare da kayan aikin vector B perpendicular zuwa vector A.
Me zai faru idan A x B mun dawo ga zama B x A ?
Da farko, bari mu zana vector B dan A da kuma kayan aikin vector A wanda yake daidai da B
Dangane da wannan adadi, za mu iya ayyana samfurin giciye tsakanin vectors B dan A (B x A) a matsayin samfurin girman vector B tare da kayan aikin vector A perpendicular zuwa vector BAn rubuta ta hanyar lissafi:
Hanyar ninka giciye A x B
Samfurin giciye samfurin vector ne, don haka samfurin yana da girma da alkibla. An samo girman samfurin vector a sama; yanzu ƙayyade alkiblarsa. Don tantance alkiblar. A x BDa farko, za mu zana vectors A da B kamar yadda aka nuna a ƙasa. Mun sanya waɗannan vectors guda biyu a cikin jirgin sama.
ninka giciye A x B an ayyana shi a matsayin vector mai layi ɗaya da layin da vector ɗin ke ciki A dan B yana nan. Girman yana iri ɗaya da AB zunubi inna. Idan C = A x B Maka C = AB zunubi inna
Arah C a tsaye zuwa ga jirgin da vector ɗin ke ciki A dan B wurin da aka samo. Za mu iya amfani da ƙa'idar hannun dama don tantance alkiblar CIdan muka riƙe yatsunmu a alkiblar da ke akasin alkiblar juyawar agogo, to alkiblar C a daidai da yadda babban yatsan yatsa ke nuna sama.
Hanyar ninka giciye B x A
Don tantance alkiblar B x ADa farko mu zana vector B dan A kamar hoton da ke ƙasa. Mun sanya waɗannan vectors guda biyu a cikin jirgin sama.
Idan C = B x A Maka C = BA sinte.
Alkiblar C tana daidai da jirgin sama inda vector ɗin yake B dan A wurin da aka samo. Za mu iya amfani da ƙa'idar hannun dama don tantance alkiblar CIdan muka riƙe yatsunmu a alkiblar da ta yi daidai da alkiblar juyawar hannuwa ta hannun agogo, to alkiblar C daidai da alkiblar babban yatsa da ke nuna ƙasa.
A x B ba daidai yake da B x ASamfurin giciye yana haifar da adadin vector, wanda banda girmansa, shi ma yana da alkibla. A cikin faɗuwar da ke sama, alkibla A x B akasin alkibla zuwa B x A.
Wasu abubuwa game da ninka giciye da kuke buƙatar sani:
1. Yawan ninkawa tsakanin ginshiƙai yana hana haɗuwa.
A x B = - B x A
Alamar korau tana nuna cewa alkiblar B a kan A x B akasin alkibla B a kan B x A.
2. Idan vectors guda biyu sun keɓance juna perpendicular to kusurwar da aka kafa ita ce 90o. Zunubi 90o = 1. Saboda haka, girman samfurin giciye tsakanin vectors A dan B zai yi kama kamar haka:
A x B = AB zunubi inna = AB ba 90o = AB
B x A = BA zunubi inna = BA ba 90o = BA
3. Idan duka vectors suna cikin alkibla ɗaya, to kusurwar da aka samar ita ce 0o.
Zunubi 0o = 0. Saboda haka, ƙimar samfurin giciye tsakanin vectors A dan B zai bayyana kamar haka.
A x B = AB zunubi theta = AB zunubi 0o = 0
B x A = BA zunubi theta = BA daidai 0o = 0
