Cov vectors hauv chav tsev - teeb meem thiab kev daws teeb meem

Cov vectors hauv chav tsev - teeb meem thiab kev daws teeb meem

1. Ib yam khoom txav mus los nrog lub zog ntawm v = (2i − 1.5j) m/s. Qhov kev hloov chaw ntawm yam khoom tom qab 4 vib nas this yog dab tsi?

Paub:

Qhov feem kab rov tav ntawm qhov ceev (v _x ) = 2 m/s

Qhov feem ntsug ntawm qhov ceev (v _y ) = 1.5 m/s

Lub sijhawm luv (t) = 4 vib nas this

Xav tau: Kev hloov chaw

Tshuaj:

Qhov tshwm sim ntawm qhov ceev (v):

Kev Hloov Chaw:

s = vt = (2.5 m/s)(4 s)

s = 10 meters

2. Vector F ₁ = 14 N thiab F ₂ = 10 N. Txheeb xyuas qhov vector tshwm sim yog tias tau hais hauv R = i + j.

Tshuaj:

Cov khoom ntawm vectors:

F _1x = (F ₁ )(cos 60 ^o ) = (14)(0.5) = -7 N (Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug))

F _1y = (F ₁ )(sin 60 ^o ) = (14)(0.5√3) = 7√3 N (Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab xis))

F2x = ₁₀ N

F2y = ₀

Cov khoom ntawm cov vectors resultant:

F _x = F _1x + F _2x + F _3x = -7 + 10 = 3 N

F _y = F _1y + F _2y + F _3y = 7√3 + 0 = 7√3 N

Tus vector tshwm sim hauv unit vector:

R = 3 i + 7√3 j

1. Ib lub vector unit yog dab tsi? tebIb lub unit vector yog ib lub vector uas muaj qhov loj ntawm 1. Feem ntau nws sawv cev rau kev taw qhia yam tsis qhia txog cov ntaub ntawv hais txog qhov loj.
2. Vim li cas cov vectors unit thiaj tseem ceeb hauv kev kawm lej vector thiab physics? tebCov vectors hauv chav yog qhov tseem ceeb vim tias lawv muab ib txoj hauv kev los piav qhia txog kev taw qhia. Lawv tuaj yeem raug ntsuas los ntawm qhov loj me los tsim ib lub vector nrog qhov ntev xav tau hauv ib qho kev taw qhia tshwj xeeb.
3. Yuav ua li cas koj thiaj tau txais ib lub vector unit los ntawm ib lub vector uas tau muab? tebIb lub vector unit nyob rau hauv qhov kev taw qhia ntawm ib lub vector muab tuaj yeem tau los ntawm kev faib lub vector los ntawm nws qhov loj.
4. Cov vectors txheem hauv Cartesian coordinates yog dab tsi, thiab lawv cov kev taw qhia yog dab tsi? tebCov vectors txheem hauv Cartesian coordinates yog i, j, Thiab k. i cov ntsiab lus nyob rau hauv qhov kev taw qhia ntawm x-axis, j cov ntsiab lus nyob rau hauv qhov kev taw qhia ntawm y-axis, thiab k cov ntsiab lus nyob rau hauv qhov kev taw qhia ntawm z-axis.
5. Ib lub vector unit puas muaj cov khoom sib xyaw uas tsis yog 1 lossis -1? tebYog. Cov khoom ntawm ib lub unit vector nyob ntawm nws qhov kev taw qhia. Tsuas yog cov unit vectors thiaj li sib phim nrog cov coordinate axes (xws li i, j, k nyob rau hauv Cartesian coordinates) yuav muaj cov khoom ntawm 1, -1, lossis 0.
6. Puas yog qhov sib ntxiv ntawm ob lub vectors hauv ib lub vector? tebTsis yog. Feem ntau, qhov sib ntxiv ntawm ob lub vectors unit tsis yog ib lub vector unit tshwj tsis yog tias ob lub vectors yog collinear thiab oppositely directed.
7. Puas siv tau ib lub vector unit los sawv cev rau ib lub vector uas muaj qhov loj sib txawv tab sis tib qho kev taw qhia? tebYog. Kev sib npaug ntawm ib lub vector unit los ntawm ib lub scalar yuav hloov nws qhov loj thaum tseem khaws nws txoj kev taw qhia tib yam.
8. Qhov loj ntawm cov khoom sib tshuam ntawm ob lub vectors unit yog dab tsi? tebQhov loj ntawm cov khoom sib tshuam ntawm ob lub vectors unit yog sib npaug rau qhov sine ntawm lub kaum sab xis ntawm lawv. Tus nqi siab tshaj plaws yog 1 thaum cov vectors yog perpendicular, thiab qhov tsawg kawg nkaus yog 0 thaum cov vectors yog parallel.
9. Vim li cas nws thiaj li hais tias cov khoom ntawm ob lub vectors muab cov cosine ntawm lub kaum sab xis ntawm lawv? tebCov mis ntawm cov dot product rau ob lub vectors yog muab los ntawm cov khoom ntawm lawv qhov loj thiab cosine ntawm lub kaum sab xis ntawm lawv. Thaum ob lub vectors yog unit vectors, lawv qhov loj yog 1, yog li cov dot product yooj yim rau cosine ntawm lub kaum sab xis.

10. Lub tswv yim ntawm ib lub unit vector txuas ntxiv mus rau hauv cov kab ke sib koom ua ke uas tsis yog Cartesian li cas? Lus Teb : Hauv cov kab ke sib koom ua ke uas tsis yog Cartesian, zoo li cov kab ke sib koom ua ke spherical lossis cylindrical, muaj cov vectors sib txawv sib raug rau txhua qhov kev taw qhia ntawm kev sib koom ua ke. Piv txwv li, hauv cov kab ke sib koom ua ke spherical, cov vectors unit yog r (kev taw qhia radial), θ (kev taw qhia lub kaum sab xis polar), thiab φ (kev taw qhia azimuthal).