Muchinjikwa chigadzirwa chevheji

Muchinyorwa chino, tichaona nzira yekuwana nayo muchinjika chigadzirwa chevheji mbiri, kupa dudziro yejometri, algebraic formula uye zvimiro zvechiito ichi, uye zvakare kuongorora muenzaniso wekugadzirisa dambudziko.

Geometric dudziro

Vector chigadzirwa chevaviri vasiri zero vectors a и b iri vector c, iyo inoratidzwa kuti [a, b] or a x b.

Vector urefu c yakaenzana nenzvimbo yeparalelogiramu yakagadzirwa uchishandisa mavheji a и b.

Muchiitiko chino, c perpendicular kune ndege mavari a и b, uye inowanikwa kuitira kuti zvishoma kutenderera kubva a к b yakaitwa counterclockwise (kubva pakuona kwekuguma kwevector).

Muchinjika chigadzirwa formula

Chigadzirwa chevectors a = {a_x; ku_y,_z} i b = {b_x; b_y,b_z} inoverengerwa uchishandisa imwe yemafomula ari pazasi:

Cross product properties

1. Chigadzirwa chemuchinjikwa chevaviri vasiri zero vectors chakaenzana ne zero kana uye chete kana mavector aya ari collinear.

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

2. Iyo module yemuchinjikwa chigadzirwa chevheji mbiri yakaenzana nenzvimbo yeparalelogiramu inoumbwa nemavheji aya.

S_Parallel = |a x b|

3. Nzvimbo yekona yakaumbwa nemavheji maviri yakaenzana nehafu yechigadzirwa chavo chevector.

S_Δ = ¹/₂ · |a x b|

4. A vector iri muchinjikwa chigadzirwa chemamwe mavheji maviri ari perpendicular kwavari.

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

Muenzaniso wedambudziko

Complete the cross product a = {2; 4; 5} и b = {9; -piri; 3}.

Sarudzo:

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