Cross ngwaahịa nke vectors

N'ime akwụkwọ a, anyị ga-atụle otu esi achọta ngwaahịa nke vector abụọ, nye nkọwa geometric, usoro algebra na njirimara nke omume a, ma nyochaakwa ihe atụ nke idozi nsogbu ahụ.

Nkọwa geometric

Ngwaahịa vector nke vector abụọ na-abụghị efu a и b bụ vector c, nke a kọwara dị ka [a, b] or a x b.

Ogologo vector c hà nhata n'akụkụ nke parallelogram a rụrụ site na iji vectors a и b.

N'okwu a, c perpendicular na ụgbọ elu nke ha nọ a и b, na dị ka obere ntụgharị si a к b emere ya na elekere elekere (site na echiche nke njedebe nke vector).

Usoro ngwaahịa gafere

Ngwaahịa nke vectors a = {a_x; ka_y,_z} i b = {b_x; b_y,b_z} na-agbakọ site na iji otu n'ime usoro ndị a:

Ngwongwo ngwaahịa gafere

1. The cross ngwaahịa nke abụọ na-abụghị efu vector bụ hà efu ma ọ bụrụ na naanị ma ọ bụrụ na ndị a vectors bụ collinear.

[a, b] = 0, ọ bụrụ a || b.

2. The modul nke cross ngwaahịa nke abụọ vectors bụ hà na ebe nke parallelogram kpụrụ ndị a vectors.

S_yiri = |a x b|

3. Mpaghara triangle kpụrụ site na vector abụọ ruru ọkara nke ngwaahịa vector ha.

S_Δ = ¹/₂ · |a x b|

4. A vector nke bụ cross ngwaahịa nke abụọ vectors ọzọ bụ perpendicular na ha.

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

Ọmụmaatụ nke nsogbu

Gbakọọ ngwaahịa obe a = {2; 4; 5} и b = {9; - abụọ; 3}.

Mkpebi:

Azịza: a x b = {19; 43; -42}.