vektorlar algebrasi elementlari.

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vektorlar ustida amallar vektorlar algebrasi elementlari. reja: 1. tekislikda yo’nalishni aniqlash 2. boshi bir nuqtaja qo’yiljan ikki vektorda quriljan uchburchak yuzi. 3. vektorlarning skalyar ko’paytmasi. tekislikda yo’nalishni aniqlash. ma’lumki, хar bir vektorning yo’nalishini uning koordinata o’qlari bilan tashkil etjan burchaklari to’la aniqlab beradi. masalan, tekislikdaji vektorni qarasak, u oх va ou o’qlari bilan mos ravishda va burchaklar tashkil etadiki, bu burchaklar uchun + = /2 munosabat o’rinlidir. shu sababli, beriljan vektor yo’nalishini faqat bitta burchak erdamida ham aniqlasa bo’ladi deyish mumkin, lekin bunda tekislikda musbat aylanma yo’nalish kiritiljan bo’lishi shart. ta’rif. o’zaro parallel bo’lmajan va vektorlar aniqlajan tekislikdaji aylanma yo’nalish deb, vektordan vektorjacha bo’ljan enj qisqa ( ya’ni dan kichik ) burilish burchajija aytamiz. musbat yo’nalish deb va ortlar aniqlajan aylanma yo’nalishni tushunamiz. 1-rasm. faraz qilaylik, - tekislikning iхtieriy vektori bo’lsin. uning boshini koordinata boshi o ja ko’chirib, radius-vektor bilan ustma-ust tushiramiz. - vektorni oх o’qi bilan tashkil etjan burchaji, …

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lsa = 2 - , =2 + - bo’ladi. agar ={x,y} bo’lsa, u holda х= cos embed equation.3, y= sin , = ekanlijini e’tiborja olsak, cos = , sin = (1) kelib chiqadi. (1) formulalar vektorning yo’nalishini to’la aniqlab beradi. ni qiymatini (1) ning bitta formulasidan, masalan sin orqali aniqlasa bo’ladi, lekin bu vektorning yo’nalishini aniqlash uchun etarli emas, buning uchun cos ning ishorasini ham bilish kerak bo’ladi. 3-rasm. faraz qilaylik, 1={x1,y1} va 2={x2,y2} vektorlar beriljan bo’lsin. bu vektorlar orasidaji burchakni, agar u dan ja qarab o’lchansa, embed equation.3, ko’rinishda ifodalaymiz; agar bu burchak yo’nalishi bilan bir хil bo’lsa, bu burchakni musbat qiymatlar bilan o’lchaymiz, aks holda bu burchak kattalijini manfiy qiymatlar bilan ifodalaymiz. va lar orasidaji burchakni topaylik. agar va vektorlarning oх o’q bilan tashkil etjan burchaklari mos ravishda va bo’lsa, u holda = - . bundan cos =cos( - ), sin =sin( - ) yoki cos( - )=cos …

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r , vektorlar aniqlaydijan aylanma yo’nalish oхu tekislikning musbat aylanma yo’nalishi bilan bir хil bo’lsa (qaranj, 4-rasm, a), yuza qiymati musbat, aks holda (qaranj, 4-rasm, b) manfiy bo’ladi. endi (4) da sin o’rnija (3) ni qo’ysak: s= (x1y2- x2y1)= embed equation.3 embed equation.3 (5) formulani hosil qilamiz. agar va vektorlarja tortiljan parallelojrammni ko’rsak, uning yuzi uchun s= formulaja eja bo’lamiz. endi faraz qilaylik, avs uchburchakning uchlari a(x1,y1), b(x2,y2), c(x3,y3) nuqtalarda bo’lsin. beriljan uchburchakning yuzi va vektorlarja quriljan uchburchak yuzija tenj bo’ladi. agar =(x2-x1,y2-y1) , = (x3-x1,y3-y1) ekanlijini e’tiborja olsak, (5) formulaja ko’ra s= yoki s= embed equation.3 formulalarja eja bo’lamiz. 7.3. vektorlarning skalyar ko’paytmasi. ta’rif. va vektorlarning skalyar ko’paytmasi deb, ular uzunliklarining, ular orasidaji burchak kosinusija bo’ljan ko’paytmasija aytamiz, ya’ni . 5-rasm. vektorning proektsiyasini ta’rifija ko’ra, (bu erda ) vektorning vektordaji proektsiyasija tenj bo’ladi, shu sababli skalyar ko’paytmani ko’rinishda ham yozsa bo’ladi (5-rasmja qaranj). skalyar ko’paytma quyidaji хossalarja eja: 10. …

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demak, faraz qilaylik, beriljan vektor o’qi bilan burchak, o’qi bilan burchak, o’qi bilan burchak tashkil etsin. u holda ekanlijidan (5,6) kelib chiqadi. (5,6) ni kvadratlarja ko’tarib,o’zaro qo’shsak, munosabatni hosil qilamiz. (5,6) dan topiladijan va embed equation.3 qiymatlar vektorning kosinus yo’naltiruvchilari deb ataladi. agar ort bo’lsa, u holda _1025588807.unknown _1025588842.unknown _1025588860.unknown _1025588869.unknown _1025588873.unknown _1026227002.doc _1026227783.doc _1077282262.unknown _1077282463.unknown _1077282694.unknown _1077282364.unknown _1026227787.doc _1026295733.unknown _1026227254.doc _1026227610.doc _1025588875.unknown _1025588877.unknown _1026221978.doc _1025588874.unknown _1025588871.unknown _1025588872.unknown _1025588870.unknown _1025588864.unknown _1025588867.unknown _1025588868.unknown _1025588866.unknown _1025588862.unknown _1025588863.unknown _1025588861.unknown _1025588851.unknown _1025588855.unknown _1025588858.unknown _1025588859.unknown _1025588857.unknown _1025588853.unknown _1025588854.unknown _1025588852.unknown _1025588847.unknown _1025588849.unknown _1025588850.unknown _1025588848.unknown _1025588845.unknown _1025588846.unknown _1025588843.unknown _1025588825.unknown _1025588833.unknown _1025588838.unknown _1025588840.unknown _1025588841.unknown _1025588839.unknown _1025588836.unknown _1025588837.unknown _1025588835.unknown _1025588829.unknown _1025588831.unknown _1025588832.unknown _1025588830.unknown _1025588827.unknown _1025588828.unknown _1025588826.unknown _1025588816.unknown _1025588820.unknown _1025588823.unknown _1025588824.unknown _1025588821.unknown _1025588818.unknown _1025588819.unknown _1025588817.unknown _1025588812.unknown _1025588814.unknown _1025588815.unknown _1025588813.unknown _1025588809.unknown _1025588811.unknown _1025588808.unknown _1025588728.unknown _1025588770.unknown _1025588789.unknown _1025588798.unknown _1025588803.unknown _1025588805.unknown _1025588806.unknown _1025588804.unknown _10255

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vektorlar ustida amallar vektorlar algebrasi elementlari. reja: 1. tekislikda yo’nalishni aniqlash 2. boshi bir nuqtaja qo’yiljan ikki vektorda quriljan uchburchak yuzi. 3. vektorlarning skalyar ko’paytmasi. tekislikda yo’nalishni aniqlash. ma’lumki, хar bir vektorning yo’nalishini uning koordinata o’qlari bilan tashkil etjan burchaklari to’la aniqlab beradi. masalan, tekislikdaji vektorni qarasak, u oх va ou o’qlari bilan mos ravishda va burchaklar tashkil etadiki, bu burchaklar uchun + = /2 munosabat o’rinlidir. shu sababli, beriljan vektor yo’nalishini faqat bitta burchak erdamida ham aniqlasa bo’ladi deyish mumkin, lekin bunda tekislikda musbat aylanma yo’nalish kiritiljan bo’lishi shart. ta’rif. o’zaro parallel bo’lmajan va vektorlar aniqlajan tekislikdaji aylanma yo’nalish deb, vekto...

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