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.