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)
Mövzu8. Müstəvi tənlikləri və onların qarşılıqlı vəziyyəti.
Müstəvi və düz xəttin qarşılıqlı vəziyyəti
Müstəvinin ümumi tənliyi.
Koordinat sisteminə nəzərən müstəvilərin yerləşməsinin xüsusi halları.
İki müstəvi arasındakı bucaq.
Müstəvi və düz xəttin qarşılıqlı vəziyyəti.
Müstəvinin normal tənliyi
Müstəvi –həndəsənin əsas anlayışlarındandır. Nəzəri cəhətcə ikiölçülü sonsuz uzunluğa malik yastı, sonsuz kiçik qalınlığa malik obyekt.
Müstəvinin tənliyi ilk dəfə olaraq A.K.Kleronun 1731-ci ildə nəşr edilmiş əsərində, müstəvinin kəsiklərdə tənliyi Q.Lamenin 1816-1818-ci illərdə çap edilmiş işlərində, normal tənliyi isə L.Qessenin 1861-ci ildəki tədqiqatlarında rast gəlinir. Müstəvinin n-ölçülü fəzada təsvirini ifadə edən tənliyi E.Kondratyev 2006-cı ildə təklif edib.
Fəzada ixtiyari nöqtəsinə və vektoruna baxaq. Müstəvidə hər hansı nöqtəsi götürək. Aydındır ki, vektoru vektoruna perpendikulyardır .
Bu tənliyi koordinatlarda yazaq:
Bu tənlik nöqtəsindən keçən vektoruna perpendikulyar olan müstəvinin tənliyidir. Bu tənliyi sadələşdirək.
ilə işarə edək. Onda alırıq:
Bu tənlik müstəvinin ümumi tənliyidir.
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