Vector - teeb meem thiab kev daws teeb meem

Vector - teeb meem thiab kev daws teeb meem

Vector thiab Scalar

1. Ntawm cov kev xaiv hauv qab no, uas yog cov khub scalar-vector ...

A. Lub zog - kev nrawm

B. Lub zog siab

C. Kev Hloov Chaw - ​​qhov ceev

D. Tam sim no hluav taws xob - siab

Tshuaj:

Lub zog = vector, kev ua kom nrawm = vector

Siab = scalar, lub zog = vector

Kev hloov chaw = vector, qhov ceev = scalar

Tam sim no hluav taws xob = scalar, siab = scalar

Cov lus teb yog B.

2.

Cov teeb meem vector thiab kev daws teeb meem 1

Cov lus teb raug yog qhia los ntawm tus lej ...

A. 1 thiab 4

B. 1 thiab 2

C. 2 thiab 3

D. 3 thiab 4

Tshuaj:

Ceev = scalar

Kev Hloov Chaw = vector

Qhov hnyav = vector

Kev nrawm = vector

Cov lus teb yog C.

Cov Cheebtsam ntawm vectors

3. Ob lub vectors, F 1 = 20 N thiab F 2 = 30 N, muaj kev taw qhia raws li qhia hauv daim duab hauv qab no. Txheeb xyuas qhov tshwm sim ntawm cov khoom ntawm vectors hauv x-axis thiab y-axis.

A. 5√3 N thiab -25 NCov teeb meem vector thiab kev daws teeb meem 2

B. -5√3 N thiab 25 N

C. 25 N thiab 5√3 N

D. 30 N thiab 25√3 N

Paub:

F1 = 20 Newtons

Lub kaum sab xis ntawm F 1 thiab x axis = 30 o

F2 = 30 Newtons

Lub kaum sab xis ntawm F2 thiab x axis =30 o

Xav tau: F x thiab F y

Tshuaj:

F 1x = F 1 cos 30 o = (20)(0.5√3) = 10√3 Newton (ntxiv lub cim vim tias taw rau +x axis)

F 1y = F 1 sin 30 o = (20)(0.5) = 10 Newtons (ntxiv lub cim vim taw tes rau +y axis)

F 2x = F 2 cos 30 o = (30)(0.5√3) = -15√3 Newton (tsis suav nrog lub cim vim tias taw rau -x axis)

F 2y = F 2 sin 30 o = (30)(0.5) = 15 Newtons (ntxiv lub cim vim taw rau +y axis)

Qhov tshwm sim ntawm x Cheebtsam:

F x = F 1x + F 2x = 10√3 N – 15√3 N = -5√3 Newtons

Qhov tshwm sim ntawm y Cheebtsam:

F y = F 1y + F 2y = 10 N + 15 N = 25 Newtons

Cov lus teb yog B.

Qhov tshwm sim ntawm ob lub vectors

4. Ob tug menyuam A thiab B thawb ib lub thaiv, yog tias A thawb lub thaiv mus rau sab qab teb nrog lub zog ntawm 400 N thiab tib lub sijhawm B thawb lub thaiv mus rau sab hnub tuaj nrog lub zog ntawm 300 N, ces txiav txim siab qhov tshwm sim ntawm lub zog A thiab B.

A. 100 N sab qab teb

B. 100 N sab hnub tuaj

C. 500 N sab qab teb sab hnub tuaj

D. 700 N sab qab teb sab hnub tuaj

Paub:

Cov teeb meem vector thiab kev daws teeb meem 3U = sab qaum teb, T = sab hnub tuaj, S = sab qab teb, B = sab hnub poob

TL = sab qaum teb sab hnub tuaj, TG = sab qab teb sab hnub tuaj, BD = sab qab teb sab hnub poob, BL = sab qaum teb sab hnub poob

A = 400 Newtons mus rau sab qab teb

B = 300 Newtons sab hnub tuaj

Xav tau: qhov loj thiab kev coj ntawm lub zog net (R)

Tshuaj:

Cov teeb meem vector thiab kev daws teeb meem 4

Cov lus teb yog C.

Qhov tshwm sim ntawm lub vector ntawm kev hloov chaw

5. Muaj ib tug neeg caij maus taus los ntawm tsev mus rau sab qaum teb 6 km ces mus rau sab hnub tuaj 8 km. Txheeb xyuas qhov chaw kawg ntawm tus neeg los ntawm qhov chaw pib.

A. 14 km sab qaum teb sab hnub tuaj

B. 14 km sab qab teb sab hnub poob

C. 10 km sab qaum teb sab hnub tuaj

D. 10 km sab qaum teb sab hnub poob

Paub:

Cov teeb meem vector thiab kev daws teeb meem 5

Xav tau: qhov loj thiab kev coj ntawm qhov kev hloov pauv tshwm sim

Tshuaj:

Cov teeb meem vector thiab kev daws teeb meem 6

Cov lus teb yog C.

6.

Vector - teeb meem thiab kev daws teeb meem 1

Raws li daim duab saum toj no, Yog tias 1 square sawv cev rau 1 km, ces tag nrho qhov kev hloov chaw yog dab tsi.

Tshuaj:

Qhov Nrug Deb = A + B + C = 6 + 6 + 2 = 14 km

Kev Hloov Chaw = R = 12 km

7. Ib lub tsheb khiav ntawm A mus rau B raws 30 km mus rau sab qaum teb, ces mus rau 60 km mus rau sab hnub tuaj, ces mus rau 110 km mus rau sab qab teb. Txheeb xyuas seb lub tsheb khiav ntawm A mus rau D li cas.

Tshuaj:

AA' = 60 km

A'D = 110 km – 30 km = 80 km

Vector - teeb meem thiab kev daws teeb meem 2

Vector - teeb meem thiab kev daws teeb meem 3

8. Ib lub tsheb mus ntawm lub nroog A mus rau lub nroog B 100 km sab qaum teb, ces mus rau lub nroog C 60 km sab hnub tuaj, thiab ces mus rau lub nroog D 20 km sab qab teb. Txheeb xyuas seb lub tsheb txav deb npaum li cas.

Tshuaj:

D'D = 60 km

AD' = 100 km – 20 km = 80 km

Vector - teeb meem thiab kev daws teeb meem 4

Vector - teeb meem thiab kev daws teeb meem 5

  1. Ib lub vector yog dab tsi?
    • teb: Ib qho vector yog ib qho ntau uas muaj ob qho tib si qhov loj (qhov loj me) thiab kev coj. Piv txwv li suav nrog qhov ceev, lub zog, thiab kev ua kom nrawm.
  2. Ib qho vector txawv ntawm ib qho scalar li cas?
    • teb: Ib qho scalar tsuas muaj qhov loj xwb, thaum ib qho vector muaj ob qho loj thiab kev coj. Piv txwv li, kub yog ib qho scalar vim nws muaj tus nqi tab sis tsis muaj kev coj, thaum qhov ceev yog ib qho vector vim nws qhia txog qhov ceev (qhov loj) hauv ib qho kev coj tshwj xeeb.
  3. Yuav ua li cas thiaj li tau sawv cev rau ib qho vector hauv daim duab?
    • teb: Ib lub vector tuaj yeem sawv cev ua duab los ntawm tus xub. Qhov ntev ntawm tus xub sawv cev rau qhov loj ntawm lub vector, thiab qhov kev taw qhia ntawm tus xub qhia txog qhov kev taw qhia ntawm lub vector.
  4. Qhov tseem ceeb ntawm tus Tsov tus tw thiab lub taub hau ntawm ib lub vector yog dab tsi?
    • teb: Tus tw yog qhov pib ntawm lub vector, thiab lub taub hau (lossis lub taub hau) yog qhov kawg. Thaum ua cov haujlwm zoo li kev ntxiv vector, tus tw ntawm ib lub vector raug muab tso rau ntawm lub taub hau ntawm lwm qhov.
  5. Cov vectors sib ntxiv ua ke li cas?
    • teb: Cov vectors raug ntxiv los ntawm kev siv txoj kev head-to-tail. Tus tw ntawm tus vector thib ob raug muab tso rau ntawm lub taub hau ntawm thawj. Tus vector uas tau txais ces raug rub los ntawm tus tw ntawm tus vector thawj mus rau lub taub hau ntawm tus vector thib ob.
  6. Qhov txawv ntawm ib qho unit vector thiab ib qho null vector yog dab tsi?
    • teb: Ib lub vector unit muaj qhov loj ntawm ib qho thiab taw tes rau hauv ib qho kev taw qhia tshwj xeeb. Nws yog siv los sawv cev rau qhov kev taw qhia ntawm ib lub vector yam tsis hais txog nws qhov loj. Ib lub vector null (lossis xoom) tsis muaj qhov loj thiab tsis muaj kev taw qhia tshwj xeeb.
  7. Yuav ua li cas thiaj muab ib lub vector sib npaug los ntawm ib lub scalar?
    • teb: Kev muab ib lub vector los ntawm ib lub scalar hloov nws qhov loj tab sis tsis hloov nws txoj kev taw qhia. Yog tias lub scalar yog qhov zoo, qhov kev taw qhia tseem zoo li qub; yog tias tsis zoo, qhov kev taw qhia rov qab.
  8. Txhais li cas rau ob lub vectors kom yog orthogonal lossis perpendicular?
    • teb: Ob lub vectors yog orthogonal lossis perpendicular yog tias lub kaum sab xis ntawm lawv yog 90 degrees. Lawv cov dot product yuav yog xoom.
  9. Yuav txiav txim siab li cas txog qhov tshwm sim ntawm ob lub vectors?
    • teb: Qhov tshwm sim yog qhov sib ntxiv ntawm ob lub vectors. Hauv daim duab, thaum cov vectors raug sawv cev ua xub, koj tuaj yeem nrhiav qhov tshwm sim los ntawm kev tso tus tw ntawm lub vector thib ob rau ntawm lub taub hau ntawm thawj thiab kos tus xub tshiab (qhov tshwm sim) los ntawm tus tw ntawm thawj lub vector mus rau lub taub hau ntawm qhov thib ob.
  10. Yog tias ib lub vector taw tes rau sab hnub tuaj nrog qhov loj ntawm 10 units, koj yuav piav qhia nws qhov sib txawv li cas?
  • teb: Qhov sib txawv ntawm cov vector no yuav muaj tib qhov loj (10 units) tab sis yuav taw tes rau hauv qhov sib txawv, piv txwv li, sab hnub poob.
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