Odgovor:
Pojasnilo:
To vemo
Torej za enote vektorjev
#barva (bela) ((barva (črna) {hati xx hati = vec0}, barva (črna) {qquad hati xx hatj = hatk}, barva (črna) {qquad hati xx hatk = -hatj}), (barva (black) {hatj xx hati = -hatk}, barva (črna) {qquad hatj xx hatj = vec0}, barva (črna) {qquad hatj xx hatk = hati}), (barva (črna) {hatk xx hati = hatj}, barva (črna) {qquad hatk xx hatj = -hati}, barva (črna) {qquad hatk xx hatk = vec0})) #
Druga stvar, ki jo morate vedeti je, da je navzkrižni produkt distributiven, kar pomeni
#vecA xx (vecB + vecC) = vecA xx vecB + vecA xx vecC # .
Za to vprašanje bomo potrebovali vse te rezultate.
# - 1, -1,2 xx 1, -2,3 #
# = (-hati - hatj + 2hatk) xx (hati - 2hatj + 3hatk) #
# = barva (bela) ((barva (črna) {- hati xx hati - hati xx (-2hatj) - hati xx 3hatk}), (barva (črna) {- hatj xx hati - hatj xx (-2hatj) - hatj xx 3hatk}), (barva (črna) {+ 2hatk xx hati + 2hatk xx (-2hatj) + 2hatk xx 3hatk})) #
# = barva (bela) ((barva (črna) {- 1 (vec0) + 2hatk qquad + 3hatj}), (barva (črna) {+ hatk qquad + 2 (vec0) - 3hati}), (barva (črna) {qquad + 2hatj qquad + 4hati qquad + 6 (vec0)})) #
# = hati + 5hatj + 3hatk #
#= 1,5,3#
Kaj je navzkrižni produkt <0,8,5> in <-1, -1,2>?
<21,-5,8> We know that vecA xx vecB = ||vecA|| * ||vecB|| * sin(theta) hatn, where hatn is a unit vector given by the right hand rule. So for of the unit vectors hati, hatj and hatk in the direction of x, y and z respectively, we can arrive at the following results. color(white)( (color(black){hati xx hati = vec0}, color(black){qquad hati xx hatj = hatk}, color(black){qquad hati xx hatk = -hatj}), (color(black){hatj xx hati = -hatk}, color(black){qquad hatj xx hatj = vec0}, color(black){qquad hatj xx hatk = hati}), (color(black){hatk xx hati = hatj}, color(black){qquad hatk xx hatj = -hati}, color(black){qquad hatk xx hatk
Kaj je navzkrižni produkt [0,8,5] in [1,2, -4]?
[0,8,5] xx [1,2, -4] = [-42,5, -8] Rezultat izdelka vecA in vecB je vecA xx vecB = || vecA || * || vecB || * sin (theta) hatn, kjer je theta pozitiven kot med vecA in vecB, in hatn je enota vektor s smerjo, podano z desnim pravilom. Za enote vektorje hati, hatj in hatk v smereh x, y in z, barva (bela) ((barva (črna) {hati xx hati = vec0}, barva (črna) {qquad hati xx hatj = hatk} , barva (črna) {qquad hati xx hatk = -hatj}), (barva (črna) {hatj xx hati = -hatk}, barva (črna) {qquad hatj xx hatj = vec0}, barva (črna) {qquad hatj xx hatk = hati}), (barva (črna) {hatk xx hati = hatj}, barva (črna) {qquad hatk xx hatj = -hati},
Kaj je navzkrižni produkt [-1,0,1] in [0,1,2]?
Prečni produkt je = 1,2 - 1,2, -1〉 Prečni produkt se izračuna z determinanto (veci, vecj, veck), (d, e, f), (g, h, i) | kjer sta, d, e, f〉 in, g, h, i〉 2 vektorja Tukaj imamo veca = 1,0 - 1,0,1〉 in vecb = ,2 0,1,2〉 Zato, | (veci, vecj, veck), (-1,0,1), (0,1,2) | = veci | (0,1), (1,2) | -vecj | (-1,1), (0,2) | + veck | (-1,0), (0,1) | = veci (-1) -vecj (-2) + veck (-1) = 1,2 - 1,2, -1〉 = vecc Preverjanje z 2 točkovnimi izdelki ,2 -1,2, -1〉. 〈- 1, 0,1〉 = 1 + 0-1 = 0 ,2 -1,2, -1〉. ,2 0,1,2〉 = 0 + 2-2 = 0 Torej je vecc pravokoten na veca in vecb