Cov vectors tsis yog cov lej ib txwm muaj, yog li ntawd kev sib npaug ib txwm tsis tuaj yeem siv ncaj qha rau lawv. Peb yuav tsum siv kev sib npaug vector. Muaj ob hom kev sib npaug vector: kev sib npaug dot thiab kev sib npaug hla. Kev sib npaug dot kuj tseem hu ua kev sib npaug scalar vim nws tsim cov lej scalar. Kev sib npaug hla kuj tseem hu ua kev sib npaug vector vim nws tsim cov lej vector. Piv txwv li, muaj ob lub vectors, uas yog A dan BKev sib npaug ntawm cov vectors A dan B tau hais nrog AB KVim tias lub arena siv cov cim qhia dot, qhov kev sib npaug no hu ua cov khoom dot. Kev sib npaug ntawm vector A dan B tau hais nrog A x BVim nws siv cov cim qhia x, ces qhov kev sib ntxiv no hu ua kev sib ntxiv hla.
Piv txwv li, muab lub vector A dan B raws li pom hauv daim duab hauv qab no. Cov khoom dot ntawm cov vectors A dan B sau ua AB (A taw tes B).
Txhawm rau txhais cov khoom dot ntawm vectors A dan B (AB), daim duab vector A thiab cov vectors Los ntawm yuas tsim ib lub kaum sab xis θ. Tom ntej no peb kos duab qhov projection ntawm vector B mus rau qhov kev taw qhia ntawm vector AQhov kev kwv yees no yog ib feem ntawm lub vector B uas yog sib luag rau lub vector A, uas yog tib qhov loj li B cos θ.
Yog li ntawd, peb txhais AB ua ib lub vector loj A muab sib npaug los ntawm cov khoom sib xyaw vector B uas yog sib npaug rau A. Kev suav lej peb tuaj yeem sau nws raws li nram no:
AB cos θ yog ib tus lej ib txwm (scalar). Yog li ntawd, cov khoom dot kuj hu ua cov khoom scalar. Yuav ua li cas yog tias cov khoom dot ntawm cov vectors A dan B tig rov qab mus rau BA ua ntej peb txhais BA, ua ntej peb kos lub projection ntawm lub vector A rau cov vectors B (saib daim duab hauv qab no).
Raws li daim duab no, peb tuaj yeem txhais tau BA ua ib lub vector loj B muab sib npaug los ntawm cov khoom sib xyaw vector A uas yog sib npaug rau B. Kev suav lej peb tuaj yeem sau nws raws li nram no:
Cov txiaj ntsig ntawm cov khoom dot AB = AB cos θ thiab qhov tshwm sim ntawm cov khoom dot BA = BA cos θVim tias AB cos θ = BA cos θ, ces nws siv tau AB = BA
Qee yam hais txog kev sib npaug ntawm cov dot uas koj yuav tsum paub:
1. Cov khoom dot ua tau raws li txoj cai commutative.
AB = BA
2. Cov khoom teev ua tau raws li txoj cai faib tawm.
A. (B + C) = AB + AC
3. Yog tias tus vector A dan B perpendicular rau ib leeg, ces qhov tshwm sim ntawm cov khoom dot AB = 0
Thaum lub vector A dan B perpendicular rau ib leeg, ces lub kaum sab xis tsim yog 90o. Cos 90o = 0. Yog li ntawd: AB = AB cos tus phauj = AB coj 90o = 0. Ntawm qhov tod tes, BA = BA cos tus phauj = BA coj 90o = 0
4. Yog tias tus vector A thiab cov vectors B ib txoj kev, yog li ntawd AB = AB coj 0o = AB
Thaum lub vector A dan B nyob rau hauv tib qho kev taw qhia, ces lub kaum sab xis tsim yog 0o. Cos 0 = 1. Yog li, AB = AB cos tus phauj = AB coj 0o = AB. Ntawm qhov tsis sib xws BA = BA cos tus phauj = BA coj 0o = BA
(Koj yuav tsum tsis txhob xav tsis thoob nrog AB dan BA. Loj AB = loj BAPiv txwv li, qhov loj ntawm lub vector A = 2. qhov loj ntawm vector B = 3. ces AB = 2.3 = 6; qhov no zoo ib yam li BA = 3.2 = 6.
5. Lwm yam mob rau ob lub vectors kom nyob rau tib qho kev taw qhia, yog tias A = B ces tau txais AA = A2 los yog BB = B2
6. Yog tias tus vector A dan B kev taw qhia sib txawv (thaum ob lub vectors nyob rau hauv qhov kev taw qhia sib txawv ces lub kaum sab xis tsim yog 180º), ces qhov tshwm sim ntawm kev sib npaug AB = AB cos 180º = AB (-1) = -AB.
Cos 180º = -1.
Piv txwv teeb meem:
Ib qho vector A muaj qhov loj ntawm 4 units thiab yog ib qho vector B muaj 3 units. Txheeb xyuas cov dot product ntawm ob lub vectors yog tias cov ces kaum uas tsim los ntawm ob lub vectors yog 60º, 90º thiab 180º.o
Kev Sib Tham
Vim AB = BA ces peb tuaj yeem xaiv siv ib qho. Piv txwv li, peb siv AB
AB = AB cos tus phauj
Loj A = 4 chav thiab loj B = 3 units.
