Nisan aya daga shimfiɗa da aya mafi kusa a 3D

Yadda ake samun kimantawa

Vekta mai tsaye ga shimfiɗa shi ne N = (A, B, C). Idan S = A² + B² + C² da r = A·Px + B·Py + C·Pz − D, aya mafi kusa ita ce Q = P − (r/S)N, nisa kuma = √(r²/S). Q tana kan shimfiɗar kuma P − Q yana tsaye gare ta. Idan P tana kan shimfiɗar tun farko, nisa sifili ne kuma Q = P. Nisa yana amfani da raka’ar wurare; Q tana cikin wannan tsarin wurare.

Aya guda da shimfiɗar Euclid guda cikakkiya marar iyaka, wadda ma’aunai suka bayyana, kawai. Ba nisa zuwa fuska mai iyaka, alwatika, polygon, yanki na layi, fuska mai lanƙwasa, jiki ko raga ba. Babu nisa mai alamar ɓangare, rarraba ɓangaren shimfiɗa, daidaita shimfiɗa da bayanai, samo ta daga aya uku, zane, wuraren ƙasa, tsara hanya, sauya raka’a, tabbatar da awo, kimanta rashin tabbas ko gwajin karo; babu garantin dacewar abubuwa ko aminci. Duba duk ma’aunai huɗu da raka’o’insu.

Duba misalin da aka cika

Misalin da muka zaɓa: shimfiɗa 2x − y + 2z = 6, P = (4, 1, 4). S = 9, r = 9 da r/S = 1, don haka Q = (2, 2, 2), nisa = 3. Sauyawa yana ba da 2·2 − 2 + 2·2 = 6. Waɗannan ƙimomin misalin lissafi ne, ba awo na gaske ko girman da ake ba da shawara ba.

Ƙimomin da aka karɓa

Shimfiɗa: A, lambar da ta ninka x

2

Shimfiɗa: B, lambar da ta ninka y

-1

Shimfiɗa: C, lambar da ta ninka z

2

Shimfiɗa: D, ɓangaren dama

6

Aya P: x

4

Aya P: y

1

Aya P: z

4

Shirya mataki na gaba

Duba matakan lissafi da kalkuleta ta yau da kullum. Kafin fassara sakamako, duba lissafin shimfiɗa, gatari da raka’o’in wurare.