Umkhiqizo ophambanayo wama-vector

Kulolu shicilelo, sizocubungula indlela yokuthola umkhiqizo wesiphambano wama-vector amabili, sinikeze incazelo yejometri, ifomula ye-algebraic kanye nezakhiwo zalesi senzo, futhi sihlaziye nesibonelo sokuxazulula inkinga.

Ukuhumusha kweJiyomethri

Umkhiqizo weVector wamavekhtha amabili angewona aziro a и b iyivekhtha c, okuchazwa ngokuthi [a, b] or a x b.

Ubude be-Vector c ilingana nendawo yepharalelogramu eyakhiwe kusetshenziswa ama-vector a и b.

Esimweni esinjalo, c perpendicular endizeni abakuyo a и b, futhi itholakala ukuze ukuzungezisa okuncane ukusuka a к b kwenziwa ngokuphambene newashi (kusukela ekugcineni kwe-vector).

Ifomula yomkhiqizo ophambene

Umkhiqizo wama-vector a = {a_x; uku_y,_z} i b = {b_x; b_y,b_z} ibalwa kusetshenziswa eyodwa yamafomula angezansi:

Izakhiwo zomkhiqizo wesiphambano

1. Umkhiqizo wesiphambano wamavekhtha amabili angewona uziro ulingana noziro uma futhi kuphela uma lawa mavekhtha kuyi-collinear.

[a, b] = 0, uma a || b.

2. Imojula yomkhiqizo wesiphambano wama-vector amabili ilingana nendawo yepharalelogramu eyakhiwe yilawa ma-vector.

S_parallel = |a x b|

3. Indawo kanxantathu eyakhiwe ama-vector amabili ilingana nengxenye yomkhiqizo wabo we-vector.

S_Δ = ¹/₂ · |a x b|

4. Ivekhtha engumkhiqizo ophambene wamanye ama-vector amabili incike kakhulu kuwo.

c ⟂ a, c ⟂ b.

5. a x b = -b x a

6. (m a) x a = a x (m b) = m (a x b)

7.a + b) x c = a x c + b x c

Isibonelo senkinga

Bala umkhiqizo wesiphambano a = {2; 4; 5} и b = {9; -okubili; 3}.

Isinqumo:

Impendulo: a x b = {19; 43; -42}.