Huahana kea o nā vectors

Ma kēia paʻi ʻana, e noʻonoʻo mākou pehea e ʻike ai i ka hua kea o nā vectors ʻelua, hāʻawi i ka wehewehe geometric, kahi ʻano algebraic a me nā waiwai o kēia hana, a me ka nānā ʻana i kahi laʻana o ka hoʻoponopono ʻana i ka pilikia.

Wehewehe geometric

Huahana Vector o ʻelua vector zero-zero a и b he vector c, ka mea i hoikeia [a, b] or a x b.

Ka lōʻihi o vector c ua like ia me ka ʻāpana o ka paralelogram i kūkulu ʻia me ka hoʻohana ʻana i nā vectors a и b.

Ma keia hihia, c ku pono i ka mokulele e noho ana a и b, a ua loaʻa i ka liʻiliʻi loa o ka huli ʻana mai a к b ua hana ʻia i ka ʻaoʻao o ka manawa (mai ka ʻike o ka hopena o ka vector).

ʻO ka hoʻohālikelike huahana keʻa

Huahana o nā vectors a = {a_x; i_y,_z} i b = {b_x; b_yna B_z} ua helu ʻia me ka hoʻohana ʻana i kekahi o nā ʻōkuhi ma lalo nei:

Nā waiwai hua kea

1. Ua like ka huina hoonui kea o na vectors ole-zero elua me ka ole ina a ina he collinear keia mau vectors.

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

2. Ua like ka module o ka hua kea o na vectors elua me ka apana o ka paralelogram i hanaia e keia mau vectors.

S_{ʻano like} = |a x b|

3. ʻO ka ʻāpana o ka huinakolu i hana ʻia e nā vector ʻelua, ua like ia me ka hapalua o kā lākou huahana vector.

S_Δ = ¹/₂ · |a x b|

4. ʻO ka vector i hua kea o nā vector ʻē aʻe ʻelua e kū pono ana iā lāua.

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

Laʻana o kahi pilikia

E helu i ka hua kea a = {2; 4; 5} и b = {9; -ʻelua; 3}.

Hoʻoholo:

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