Umkhiqizo oxubile usebenzisa izingxenye ze-vector zeyunithi

Izinto Zokuphindaphinda Ezihlanganisiwe Ezisebenzisa Izingxenye I-Unit Vector

Singabala umkhiqizo oxubile ngqo uma sazi izingxenye zamavektha. Ukuhleleka kuyafana nokuthi umkhiqizo wamachashaziOkokuqala, senza ukuphindaphinda phakathi kwamavektha eyunithi. i, j dan kUmkhiqizo wevektha phakathi kwamavektha eyunithi efanayo ungu-zero.

i x i = j x j = k x k = 0

Ngokubhekisela ku-equation yokuphindaphinda kwevektha etholakale ngaphambilini (A x B = AB Isono θ) kanye nempahla evimbela ukuguquguquka kwe- ukuphindaphinda kwevektha (A x B = - B x A), bese sithola:

i x j = -j x i = k

j x k = -k x j = i

k x i = -i x k = j

Manje sesisho i-vector A dan B zibe izingxenye zayo, zihlukanise ukuphindaphinda kwayo bese zisebenzisa ukuphindaphinda kwama-vector ayo eyunithi.

A x B= (A_xi + A_yj + A_zk) x (B_xi + B_yj + B_zk)

A x B = A_xi x B_xi + A_xi x B_yj + A_xi x B_zk +

A_yj x B_xi + A_yj x B_yj + A_yj x B_zk +

A_zk x B_xi + A_zk x B_yj + A_zk x B_zk

A x B = A_xB_x (i x i) + A_xB_y (i x j) + A_x B_z (i x k) +

A_yB_x (j x i) + A_yB_y (j x j) + A_yB_z (j x k) +

A_zB_x (k x i) + A_zB_y (k x j) + A_zB_z (k x k)

UKarena i x i = j x j = k x k = 0 dan i x j = -j x i = k,  j x k = -k x j = i, k x i = -i x k = j, ngakho-ke:

A x B = A_xB_x (0) + A_xB_y (k+ A_x B_z (-j+

A_yB_x (-k+ A_yB_y (0) + A_yB_z (i+

A_zB_x (j+ A_zB_y (-i+ A_zB_z (0)

A x B = A_xB_y (k+ A_x B_z (-j+

A_yB_x (-k+ A_yB_z (i+

A_zB_x (j+ A_zB_y (-i)

A x B = A_xB_y (k+ A_x B_z (-j+ A_yB_x (-k+ A_yB_z (i+ A_zB_x (j+ A_zB_y (-i)

A x B = ((A_yB_z - A_zB_y)i + (A_zB_x - A_x B_z)j + (A_xB_y - A_yB_x )k

Uma C = A x B bese kuba izingxenye ze C yilezi ezilandelayo:

_Cx = A_yB_z - A_zB_y

_Cy = A_zB_x - A_x B_z

_Cz = A_xB_y - A_yB_x