Kev sib tham txog cov vectors hauv kev lej yog qhov sib cais tsis tau ntawm kev sib tham txog Cartesian coordinate system. Lub Cartesian coordinate system yog lub system siv ntau tshaj plaws rau kev ua qauv thiab kev txheeb xyuas ntau yam xwm txheej hauv ob thiab peb-seem. Hauv tsab xov xwm no, peb yuav tshawb nrhiav lub tswv yim ntawm cov vectors sib npaug hauv cov ntsiab lus ntawm Cartesian coordinate system.
Kev Taw Qhia Txog Vectors Hauv Cartesian Coordinate System
Hauv ib lub Cartesian coordinate system, txhua lub ntsiab lus hauv qhov chaw ob-seem tuaj yeem sawv cev ua ib khub txiav txim (x, y), qhov twg x yog qhov sib koom ua kab rov tav thiab y yog qhov sib koom ua ntsug. Rau qhov chaw peb-seem, peb muaj triplet (x, y, z). Ib lub vector hauv cov ntsiab lus no yog ib qho lej uas muaj ob qho tib si qhov loj (lossis ntev) thiab kev coj.
Ib lub vector nyob rau hauv qhov chaw ob-seem feem ntau yog sawv cev raws li \(\vec{v}\) = (v_x, v_y), qhov twg \(v_x\) thiab \(v_y\) yog cov khoom ntawm lub vector raws x-axis thiab y-axis, raws li. Hauv qhov chaw peb-seem, ib lub vector yog sawv cev raws li \(\vec{v}\) = (v_x, v_y, v_z).
Lub Tswv Yim ntawm Vector Equivalence
Ob lub vectors raug hais tias sib npaug yog tias lawv muaj tib qhov loj thiab tib qho kev taw qhia, tsis hais lawv qhov chaw pib. Hauv kev suav lej, ob lub vectors \(\vec{u}\) = (u_x, u_y) thiab \(\vec{v}\) = (v_x, v_y) raug hais tias sib npaug yog tias:
1. \(u_x = v_x\)
2. \(u_y = v_y\)
Yeej, cov vectors tsis khi rau ib qho chaw pib tshwj xeeb. Ob lub vectors tuaj yeem tso rau txhua qhov chaw hauv qhov chaw, tab sis yog tias lawv muaj tib qho kev taw qhia thiab qhov loj, lawv tseem suav tias yog sib npaug, lossis sib npaug. Qhov no yog ib qho tseem ceeb uas ua rau cov vectors yog ib qho cuab yeej siv tau ntau yam hauv kev lej thiab physics.
Kev Piv Txwv Txog Geometric
Xav tias peb muaj ob lub vectors \(\vec{u}\) = (3, 4) thiab \(\vec{v}\) = (3, 4). Ob lub vectors no, thaum pom hauv Cartesian coordinate system, yuav sawv cev rau cov xub uas nyob rau tib qho kev taw qhia thiab muaj tib qhov ntev, txawm tias lawv yuav pib los ntawm ntau qhov chaw sib txawv. Yog li, yog tias peb kos \(\vec{u}\) los ntawm keeb kwm (0, 0) mus rau qhov chaw (3, 4) thiab \(\vec{v}\) los ntawm ntau qhov chaw sib txawv, hais tias (1, 1), mus rau qhov chaw (4, 5), ob lub vectors no tseem sib npaug vim lawv muaj tib qho kev taw qhia thiab qhov loj.
Kev Sawv Cev Vector Sib Npaug Hauv Kev Ua lej
Hauv kev lej, cov vectors sib npaug ua raws li cov hauv paus ntsiab lus hauv qab no:
- Yog tias \(\vec{v}\) = (v_x, v_y) yog ib qho vector, ces txhua qhov vector sib npaug rau \(\vec{v}\) tuaj yeem tau txais los ntawm kev ntxiv tib lub vector txhais lus rau nws qhov pib thiab qhov kawg.
- Yog tias \(\vec{v_1}\) = (v_{1x}, v_{1y}) thiab \(\vec{v_2}\) = (v_{2x}, v_{2y}) yog ob lub vectors sib npaug, ces muaj ib lub vector tas mus li \(\vec{k}\) = (k_x, k_y) xws li:
\[
\vec{v_1} = \vec{v_2} + \vec{k} – \vec{k}
\]
Qhov kev faib ua feem no tuav hauv qhov chaw n-dimensional thiab hais txog qhov tseeb tias cov vectors yog qhov tseem ceeb hais txog qhov sib txawv ntawm qhov chaw, tsis yog qhov chaw lawv tus kheej.
Kev Siv Cov Vectors Sib Npaug Hauv Physics
Hauv kev kawm txog physics, lub tswv yim ntawm cov vectors sib npaug yog qhov tseem ceeb heev, tshwj xeeb tshaj yog hauv kev tshuaj xyuas lub zog, qhov ceev, thiab lub zog. Piv txwv li, cov zog ua haujlwm ntawm ib qho chaw hauv ib yam khoom tuaj yeem txhais tau (ua cov vectors sib npaug) yog tias lawv tsim cov txiaj ntsig zoo ib yam hauv kev nrawm lossis kev hloov pauv hauv lub zog.
Piv txwv ntawm daim ntawv thov:
1. Cov Zog Sib Npaug thiab Cov Vectors:
Hauv kev kawm txog tshuab hluav taws xob, yog tias lub zog F raug sawv cev ua ib lub vector thiab siv rau ntawm ib qho ntawm ib yam khoom, peb tuaj yeem txav qhov chaw siv lub zog los ntawm qhov deb sib npaug. Qhov no yog qhov tseem ceeb hauv kev xam cov sijhawm ntawm lub zog lossis torques, qhov twg cov khoom sib npaug ntawm lub zog siv los daws cov teeb meem tshuab.
2. Ceev:
Qhov ceev ua ib lub vector qhia txog kev coj thiab qhov ceev ntawm ib yam khoom txav mus los. Piv txwv li, qhov ceev ntawm lub tsheb txav mus rau sab hnub tuaj ntawm 60 km / h tuaj yeem sawv cev ua lub vector (60, 0) yog tias x-axis taw rau sab hnub tuaj. Txhua lub vectors sib npaug piav qhia txog cov xwm txheej txav mus los zoo ib yam, txawm tias lawv cov ntsiab lus pib sib txawv, piv txwv li, (1, 1) txog (61, 1).
Cov Coordinates Homogeneous thiab Equivalent Vectors
Hauv qhov chaw peb-seem, peb kuj feem ntau siv cov kev sib koom ua ke sib xws los nthuav peb qhov kev tshuaj xyuas. Lub kaw lus no qhia txog lub matrix operator projection matrix, uas ua rau peb nkag siab dav dua txog cov vectors sib npaug. Cov kev sib koom ua ke sib xws feem ntau siv hauv cov duab computer los ua kom yooj yim rau kev hloov pauv geometric xws li kev tig, kev txhais lus, thiab kev ntsuas. Hauv cov ntsiab lus no, cov vectors sib xws tso cai rau peb ua cov kev tswj hwm sib xws thiab zoo nkauj ntawm Cartesian coordinates.
Xaus
Cov vectors sib npaug hauv Cartesian coordinate system yog lub tswv yim tseem ceeb uas tsim lub hauv paus ntawm ntau daim ntawv thov lej thiab physics. Kev nkag siab txog lub tswv yim no suav nrog kev paub tias ob lub vectors sib npaug yog tias lawv muaj tib qho kev taw qhia thiab qhov loj, txawm tias lawv cov ntsiab lus pib yuav txawv. Kev sawv cev lej ntawm cov vectors sib npaug qhia tau hais tias cov khoom no tso cai rau kev txav cov ntsiab lus pib thiab xaus ntawm cov vectors yam tsis hloov lawv cov khoom tseem ceeb.
Kev siv lub tswv yim no hauv ntau qhov chaw, xws li physics, qhia txog qhov tseem ceeb ntawm kev nkag siab txog kev tshawb fawb vector rau kev tshuaj xyuas ntxiv. Hauv lub ntiaj teb tiag tiag, lub tswv yim ntawm cov vectors sib npaug tso cai rau kev suav yooj yim dua ntawm cov zog, qhov ceev, thiab ntau lwm yam ntawm mechanics thiab kinematics.
Nrog lub peev xwm los sawv cev thiab tswj cov vectors hauv Cartesian coordinate system, peb tuaj yeem ua qauv thiab tshuaj xyuas ntau yam teeb meem nyuaj thiab cov kab ke nrog qib siab ntawm kev raug thiab raug. Qhov no ua rau lub tswv yim ntawm cov vectors sib npaug yog qhov tseem ceeb thiab txaus nyiam hauv kev kawm lej thiab physics.
