Cov txheej txheem:
Video: Dab tsi yog cov khoom ntawm dot khoom?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2024-01-18 08:15
Cov khoom dot ua tiav cov khoom nram qab no yog tias a, b, thiab c yog cov vectors tiag tiag thiab r yog scalar
- Commutative: uas ua raws li lub ntsiab lus (θ yog lub kaum sab xis ntawm a thiab b):
- Distributive tshaj vector ntxiv:
- Bilinear:
- Scalar kev sib npaug:
Tom qab ntawd, ib tug kuj yuav nug, dab tsi yog 4 yam khoom ntawm dot khoom?
Cov khoom ntawm Dot Khoom
- u·v = |u||v| cov θ
- u·v = v·u.
- u · v = 0 when u and v are orthogonal.
- 0 · 0 = 0.
- |v|2 = v · v.
- a (u·v) = (a u) · v.
- (au + bv) · w = (au) · w + (bv) · w.
Ib tug kuj yuav nug, dab tsi yog cov khoom ntawm cov khoom ntoo khaub lig? Cov khoom ntawm Cross Product:
- Qhov ntev ntawm tus ntoo khaub lig khoom ntawm ob vectors yog.
- Qhov ntev ntawm tus ntoo khaub lig khoom ntawm ob vectors yog sib npaug rau thaj tsam ntawm parallelogram txiav txim los ntawm ob vectors (saib daim duab hauv qab).
- Anticommuativity:
- Multiplication los ntawm scalar:
- Kev faib tawm:
Ib yam li ntawd, koj tuaj yeem nug, dab tsi yog cov khoom lag luam txhais li cas?
A dot khoom yog a scalar nqi ntawd yog cov tshwm sim los ntawm kev ua haujlwm ntawm ob vectors nrog tib tus lej ntawm cov khoom. Muab ob vectors A thiab B txhua nrog n Cheebtsam, qhov dot khoom yog xam li: A · B = A1B1 + + A B . Cov dot khoom yog li no sum ntawm cov cov khoom ntawm txhua yam ntawm ob lub vectors.
Dab tsi yog cov yam ntxwv ntawm vectors?
Algebraic Properties of Vectors
- Commutative (vector) P + Q = Q + P.
- Associative (vector) (P + Q) + R = P + (Q + R)
- Additive yog leejtwg Muaj ib tug vector 0 xws li.
- Additive inverse Rau tej P muaj vector -P xws li P + (-P) = 0.
- Distributive (vector) r(P + Q) = rP + rQ.
- Distributive (scalar) (r + s) P = rP + sP.
- Associative (scalar) r(sP) = (rs)P.
Pom zoo:
Dab tsi yog qhov me me ntawm cov khoom uas khaws cov khoom ntawm lub caij?
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