LifeTally
Faɗin alwatika daga maki uku
Menene faɗin alwatikarka mai alama da marar alama, kuma jerin makinta yana bin agogo, akasin agogo ko layi ɗaya?
Shigar da maki uku na tsarin Kartesi domin samun faɗi biyu da alkiblar jerin kusurwoyi.
Maki uku naka
Yi amfani da gatari iri ɗaya na Kartesi masu haɗuwa a kusurwar dama, sikeli iri ɗaya da raka'ar ma'auni ɗaya. x tabbatacce yana dama, y tabbatacce sama. Shigar da lambobin goma-goma, ba a/b ba. Ana buƙatar duk ma'aunai shida.
Yadda ake samun kimantawa
D = (xB − xA)(yC − yA) − (yB − yA)(xC − xA). Faɗi mai alama D/2 ne; marar alama |D|/2 ne. A waɗannan gatari, D tabbatacce na nufin akasin agogo, korau bin agogo, sifili kuma maki a layi ɗaya ko sun haɗu. Maki maimaitattu ko a layi ɗaya ingantattu ne da faɗi sifili. Rarrabawa na amfani da ainihin bambance-bambance da ninkawar ƙimar lambobin da aka karɓa, ba tare da sassaucin kusa da sifili ba.
A = (xA, yA); B = (xB, yB); C = (xC, yC)
D = (xB − xA)(yC − yA) − (yB − yA)(xC − xA)
S = D ÷ 2; |S| = |D| ÷ 2Maki uku na lambobi na gaske a shimfiɗa kawai, a gatari na kusurwar dama da sikeli ɗaya. Ba ya lissafa faɗin ƙasa ta taswira, saman ƙwallo ko 3D, tsawon gefe, kusurwa, kewaye, cibiyar faɗi, zane, gwajin maki a ciki ko sauya raka'a. Ba ya tabbatar da awo, ƙiyasta rashin tabbas ko ba da tabbacin sakamakon safiyon ƙasa, na zahiri ko aminci. Ainihin alaƙar lambobin da aka karɓa ba hujja ba ce ga abubuwan da aka auna.
OpenStax: determinanti da faɗin alwatika ↗Wolfram: tabbatacciyar alkiblar maki ↗
Duba misalin da aka cika
Misalin da muka zaɓa: A = (−2, 1), B = (3, −1), C = (1, 4). Bambance-bambancen gefuna su ne (5, −2) da (3, 3); D = 5×3 − (−2)×3 = 21. Faɗi biyun 10.5 raka'ar ma'auni² ne; jerin yana akasin agogo. Waɗannan lambobin misalin lissafi ne, ba ƙa'idoji ko hasashe ba.
Ƙimomin da aka karɓa
- Maki A: ma'aunin x
- -2
- Maki A: ma'aunin y
- 1
- Maki B: ma'aunin x
- 3
- Maki B: ma'aunin y
- -1
- Maki C: ma'aunin x
- 1
- Maki C: ma'aunin y
- 4
Shirya mataki na gaba
Yi amfani da kalkuletar gama-gari don lissafi dabam. Duba jerin maki, gatarin da ake nufi da raka'o'in ma'auni.
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