Hla cov khoom ntawm vectors

Hauv kev tshaj tawm no, peb yuav xav txog yuav ua li cas thiaj nrhiav tau tus ntoo khaub lig khoom ntawm ob vectors, muab ib tug geometric txhais, ib tug algebraic formula thiab cov khoom ntawm qhov kev txiav txim, thiab kuj soj ntsuam ib tug piv txwv ntawm kev daws teeb meem.

Geometric txhais lus

Vector khoom ntawm ob lub vectors uas tsis yog xoom a и b yog vector c, uas yog denoted li [a, b] or a x b.

Vector ntev c yog sib npaug rau thaj tsam ntawm parallelogram tsim siv cov vectors a и b.

Nyob rau hauv cov ntaub ntawv no, c perpendicular rau lub dav hlau uas lawv nyob a и b, thiab nyob rau hauv thiaj li hais tias qhov tsawg tshaj plaws kev sib hloov los ntawm a к b tau ua counterclockwise (los ntawm qhov pom ntawm qhov kawg ntawm vector).

Hla cov khoom formula

Cov khoom siv vectors a = {a_x; rau_y,_z}i b = {b_x; b_yb_z} yog suav nrog ib qho ntawm cov qauv hauv qab no:

Hla cov khoom zoo

1. Cov khoom hla ntawm ob lub vectors tsis yog xoom yog sib npaug rau xoom yog tias thiab tsuas yog cov vectors yog collinear.

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

2. Lub module ntawm tus ntoo khaub lig khoom ntawm ob vectors yog sib npaug rau thaj tsam ntawm parallelogram tsim los ntawm cov vectors.

S_{thaum uas tig mus} = =a x b|

3. Lub cheeb tsam ntawm ib daim duab peb sab tsim los ntawm ob vectors yog sib npaug rau ib nrab ntawm lawv cov khoom vector.

S_Δ = ¹/₂ · |a x b|

4. Ib tug vectors uas yog ib tug cross khoom ntawm ob lwm vectors yog perpendicular rau lawv.

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 (ib.a + b) x c = a x c + b x c

Piv txwv ntawm qhov teeb meem

Muab xam cov khoom hla a = {2; 4; 5} и b = {9; - ob; 3}.

Kev txiav txim siab:

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