Dot Product vs Cross Product
Dot cov khoom thiab cov khoom hla yog ob txoj haujlwm ua lej siv hauv vector algebra, uas yog ib qho tseem ceeb heev hauv algebra. Cov ntsiab lus no tau siv dav hauv kev lag luam xws li electromagnetic field theory, quantum mechanics, classical mechanics, relativity and many other fields in physics and mathematics. Hauv tsab xov xwm no, peb yuav tham txog dab tsi cov khoom lag luam thiab cov khoom hla yog, lawv cov ntsiab lus thiab kev siv, qee qhov kev sib raug zoo ntawm cov khoom dot thiab cov khoom hla, thiab thaum kawg qhov sib txawv ntawm cov khoom dot thiab cov khoom hla.
Dot Product
Dot khoom, tseem hu ua cov khoom scalar, yog tus neeg siv lej siv hauv vector algebra. Cov khoom dot ntawm ob vectors A thiab B yog txhais tias | A||B| Cos (θ), qhov twg θ yog lub kaum sab xis ntsuas ntawm A thiab B. Nws tuaj yeem pom tseeb tias tus nqi ntawm cov khoom dot yog tus nqi scalar; yog li ntawd, cov khoom dot tseem hu ua cov khoom scalar. Cov khoom dot yields tus nqi siab tshaj plaws thaum ob lub vectors sib npaug rau ib leeg. Qhov tsawg kawg nkaus tus nqi ntawm cov khoom dot yog thaum ob vectors yog antiparallel. Cov khoom dot tuaj yeem siv los ua qhov projection ntawm vector hauv ib qho kev qhia; rau qhov no, lub vector thib ob yuav tsum yog lub tsev vector hauv qhov xav tau. Cov khoom dot kuj tseem muaj txiaj ntsig zoo hauv kev noj thaj chaw sib xyaw rau Gauss 'theorem. Nws kuj tseem ua lub luag haujlwm hauv kev ua haujlwm sib txawv. Cov khoom siv dot kuj tseem siv los suav cov haujlwm ua tiav hauv qhov chaw quab yuam.
Cross Product
Cross khoom, tseem hu ua vector khoom, yog kev ua lej siv hauv vector algebra. Tus ntoo khaub lig khoom nruab nrab ntawm ob vectors A thiab B yog txhais li |A||B| Sin (θ) N, qhov twg θ yog lub kaum sab xis ntawm A thiab B, thiab N yog chav tsev ib txwm vector rau lub dav hlau uas muaj A thiab B. Cov kev taw qhia ntawm N yog txiav txim siab los ntawm txoj cai ntawm tes ntsia hlau los ntawm kev coj ntawm A mus rau B. Lub modulus ntawm cov khoom dot yog qhov siab tshaj plaws thaum lub kaum sab xis ntawm A thiab B yog 90 degrees (π/2 radians). Tus ntoo khaub lig khoom yog siv los xam cov curl ntawm ib tug vector teb. Nws kuj yog siv los xam cov angular momentum, angular tshaj tawm thiab lwm yam khoom ntawm angular motion.
Dot Product thiab Cross Product yog dab tsi?
• Dot khoom yields tus nqi scalar, whereas tus ntoo khaub lig khoom yields ib vector.
• Cov khoom ntoo khaub lig siv tus nqi siab tshaj plaws thaum ob lub vectors nyob rau ib leeg, tab sis cov khoom dot siv qhov siab tshaj plaws thaum ob lub vectors sib npaug rau ib leeg.
• Dot khoom yog siv los xam qhov sib txawv ntawm qhov chaw vector, tab sis cov khoom hla yog siv los xam cov curl ntawm vector teb.
