Zvinhu zveKuwanza Dot Uchishandisa Zvikamu zveVector Unit
Tinogona kuverenga chigadzirwa chescalar zvakananga kana tichiziva zvikamu zve x, y uye z zvemavector A na B (mavector anozivikanwa).
Kuti tiite chigadzirwa chedot nenzira iyi , tinotanga taita chigadzirwa chedot chemayuniti vectors, tobva taratidza mavectors A naB muzvikamu zvavo, tobva tabvisa chigadzirwa toshandisa chigadzirwa cheyuniti vectors.
Mavector eyuniti i , j na k akaenzana, zvichiita kuti kuverenga kuve nyore. Tichishandisa scalar multiplication equation yakawanikwa pamusoro apa ( AB = AB cos theta ) tinowana:
i. i = j. j = k. k = (1)(1) cos 0 = 1
i. j = i. k = j. k = (1)(1) cos 90 o = 0
Iye zvino tinoratidza mavector A naB maererano nezvikamu zvavo, tinoparadza chigadzirwa chavo uye tinoshandisa chigadzirwa chevectors dzeyuniti.
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)
Nokuti i . i = j . j = k . k = 1 uye i . j = i . k = j . k = 0, zvino:
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 By y (1) + 0 +
0 + 0 + A z B z (1)
A . B = AxBx + AyBy + AzBz
Zvichibva pamhedzisiro yekuverenga uku, zvinogona kugumiswa kuti chigadzirwa chescalar kana chigadzirwa chedot chemavector maviri ndiwo huwandu hwezvigadzirwa zvezvikamu zvavo zvakafanana.
Muenzaniso Mubvunzo 1:
Vektori hombe A dhani B zvakateerana 5 ne4, sezvakaratidzwa mumufananidzo uri pazasi. Kona yakagadzirwa i90oZviverengere chigadzirwa chine madotsi mavector ese ari maviri.
Kukurukurirana
Tisati taverenga dot product yemavectors A naB, tinofanira kutanga taziva zvikamu zvevector yechipiri.
A x = (5) cos 0 o = (5) (1) = 5
A y = (5) chivi 0 o = (5) (0) = 0
A z = 0
B x = (4) cos 90 o = (4) (0) = 0
B y = (4) chivi 90 o = (4) (1) = 4
B z = 0
Vector A ine zvikamu zvevector chete pa x-axis uye vector B ine zvikamu zvevector chete pa y-axis. Z chikamu hachina zero nekuti mavector A na B ari mu xy plane.
Iye zvino tava kuverenga chigadzirwa chedoti pakati pemavekitari A naB tichishandisa equation yechigadzirwa chedoti nemavekitari ezvikamu:
A. B = Ax Bx + AyBy + AzBz
A. B = (5) (0) + (0) (4) + 0
A. B = 0 + 0 + 0
A. B = 0
Ngatizvienzanise nenzira yekutanga
AB = AB cos theta
AB = (4)(5) cos 90
AB = (4) (5) (0)
AB = 0
Mhedzisiro yacho yakafanana.
Muenzaniso Mubvunzo 2:
Vektori hombe A dhani B dziri 5 uye 4 zvichiteerana, sezvakaratidzwa mumufananidzo uri pazasi. chigadzirwa chine madotsi mavector ese ari maviri, kana kona yakagadzirwa iri 30o
Kukurukurirana
Tisati taverenga dot product yemavectors A naB, tinofanira kutanga taziva zvikamu zvevector yechipiri.
Chikamu che z chiri zero nekuti mavector A na B ari mu xy plane.
Iye zvino tava kuverenga chigadzirwa chedoti pakati pemavekitari A naB tichishandisa equation yechigadzirwa chedoti nemavekitari ezvikamu:
Enzanisa nenzira yekutanga.
