Wax soo saarka xididdada

Daabacaaddan, waxaan ka fiirsan doonaa sida loo helo badeecada isdhaafsan ee laba qaybood, bixino tafsiir joomatari, qaaciidada aljabrada iyo sifooyinka ficilkan, iyo sidoo kale falanqaynta tusaalaha xallinta dhibaatada.

Tafsiir joomatari

Wax soo saarka Vector ee laba qaybood oo aan eber ahayn a и b waa vector c, kaas oo lagu tilmaamay sida [a, b] or a x b.

Dhererka vector c waxay la mid tahay aagga barbar-dhigga ee la dhisay iyadoo la adeegsanayo vectors a и b.

Kiiskan, c siman diyaaradda ay ku jiraan a и b, waxayna ku taallaa si uu wareegtada ugu yar ka yimaado a к b waxaa la sameeyay saacada ka soo horjeeda (marka laga eego dhanka dhamaadka faleebada).

Ka gudub caanaha alaabta

Wax soo saarka vectors a = {a_x; ku_y,_z} i b = {b_x; b_y,b_z} waxaa lagu xisaabiyaa iyadoo la isticmaalayo mid ka mid ah hababka hoose:

Ka gudub guryaha alaabta

1. Wax soo saarka isdhaafka ah ee laba qaybood oo aan eber ahayn waxay le'eg tahay eber haddii iyo kaliya haddii vectoryadani yihiin collinear.

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

2. Module ka mid ah badeecada iskutallaabta ee labada qaybood waxay la mid tahay aagga barbar-dhigga ee ay sameeyeen vectors-yadan.

S_{isku midka ah} = |a x b|

3. Baaxadda saddexagalka ee ay sameeyeen laba qaybood waxay la mid tahay kala badh wax soo saarkooda.

S_Δ = ¹/₂ · |a x b|

4. Vector ka ah wax-soo-saarka laba qaybood oo kale ayaa ku toosan iyaga.

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

Tusaale dhibaato

Xisaabi badeecada isdhaafka ah a = {2; 4; 5} и b = {9; -laba; 3}.

Go'aanka:

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