Qalabka Isku-dhufashada Dhibcaha iyadoo la adeegsanayo Qaybaha Vektor- ka Cutubka
Waxaan si toos ah u xisaabin karnaa badeecada scalar-ka haddii aan naqaanno qaybaha x, y iyo z ee vectors-ka A iyo B (vectors-ka la yaqaan).
Si aan sidan ugu sameyno badeecad dhibic ah, marka hore waxaan sameynaa badeecad dhibic ah oo ka mid ah vector-yada cutubka, ka dibna waxaan ku muujineynaa vector-yada A iyo B qaybahooda, waxaan burburineynaa badeecada oo waxaan isticmaaleynaa badeecada vector-yada cutubka.
Vectors-ka cutubyada i , j, iyo k waa kuwo is dul saaran, taasoo sahlaysa xisaabinta. Annagoo adeegsanayna isle'egta isku dhufashada scalar ee kor ku xusan ( AB = AB cos theta ), waxaan helnaa:
i. i = j. j = k. k = (1)(1) cos 0 = 1
i. j = i. k = j. k = (1)(1) cos 90 o = 0
Hadda waxaan ku muujineynaa vektorrada A iyo B marka loo eego qaybahooda, waxaan burburineynaa badeecadooda oo waxaan isticmaaleynaa badeecada vektorrada cutubyada.
A . B = Axi . Bxi + Axi . Byj + Axi . Bzk +
Ayj . Bxi + Ayj . Byj + Ayj . Bzk +
Azk . Bxi + Azk . Byj + Azk . Bzk
A . B = AxBx (i . i) + AxBy (i . j) + Ax Bz (i . k) +
AyBx (j . i) + AyBy (j . j) + AyBz (j . k) +
AzBx (k . i) + AzBy (k . j) + AzBz (k . k)
Sababtoo ah i . i = j . j = k . k = 1 iyo i . j = i . k = j . k = 0, ka dibna:
A . B = AxBx (1) + AxBy (0) + Ax Bz (0) +
AyBx (0) + AyBy (1) + AyBz (0) +
AzBx (0) + AzBy (0) + AzBz (1)
A. B = A x B x (1) + 0 + 0 +
0 + A y B y (1) + 0 +
0 + 0 + A z B z (1)
A . B = AxBx + AyBy + AzBz
Iyada oo ku saleysan natiijooyinka xisaabintan, waxaa lagu soo gabagabeyn karaa in badeecada scalar ama wax soo saarka dhibcaha ee laba vectors ay tahay wadarta wax soo saarka qaybaha isku midka ah.
Su'aal Tusaale 1aad:
Vektor weyn A dan B siday u kala horreeyaan waa 5 iyo 4, sida ka muuqata sawirka hoose. Xagasha la sameeyay waa 90oTiri badeecad dhibic ah labada vectors.
Dood
Kahor inta aynaan xisaabin wax soo saarka dhibcaha ee vektorrada A iyo B, marka hore waxaan u baahanahay inaan ogaano qaybaha vektorrada labaad.
A x = (5) cos 0 o = (5) (1) = 5
A y = (5) dembi 0 o = (5) (0) = 0
A z = 0
B x = (4) cos 90 o = (4) (0) = 0
B y = (4) dembi 90 o = (4) (1) = 4
B z = 0
Vektor A wuxuu leeyahay qaybo vektor ah oo ku yaal dhidibka x, vektor B- na wuxuu leeyahay qaybo vektor ah oo ku yaal dhidibka y. Qaybta z waa eber sababtoo ah vektor A iyo B waxay ku jiraan diyaaradda xy.
Hadda waxaan xisaabinaynaa badeecada dhibcaha u dhaxaysa vektors A iyo B annagoo adeegsanayna isla'egta wax soo saarka dhibcaha oo leh vektors-ka qaybaha:
A. B = Ax Bx + AyBy + AzBz
A. B = (5) (0) + (0) (4) + 0
A. B = 0 + 0 + 0
A. B = 0
Aan barbar dhigno habka ugu horreeya
AB = AB cos theta
AB = (4)(5) cos 90
AB = (4) (5) (0)
AB = 0
Natiijadu waa isku mid.
Su'aal Tusaale 2aad:
Vektor weyn A dan B waa 5 iyo 4 siday u kala horreeyaan, sida ka muuqata sawirka hoose. Xisaabi badeecad dhibic ah labada vectors, haddii xagasha la sameeyay ay tahay 30o
Dood
Kahor inta aynaan xisaabin wax soo saarka dhibcaha ee vektorrada A iyo B, marka hore waxaan u baahanahay inaan ogaano qaybaha vektorrada labaad.
Qaybta z waa eber sababtoo ah vektorrada A iyo B waxay ku jiraan diyaaradda xy.
Hadda waxaan xisaabinaynaa badeecada dhibcaha u dhaxaysa vektors A iyo B annagoo adeegsanayna isla'egta wax soo saarka dhibcaha oo leh vektors-ka qaybaha:
Isbarbardhig habka ugu horreeya.
