Ivektha yeyunithi

Ukuqonda Ama-Unit Vectors 

Ivektha yeyunithi iyivektha enobukhulu obungu-1. Ivektha yeyunithi ayinawo amayunithi futhi isebenza ukukhombisa isiqondiso esikhaleni. Ukuze ihlukaniswe nevektha evamile, inyatheliswa ngokugqamile (ngombhalo ophrintiwe) noma kufakwe uphawu lwe-^ ngaphezu kwayo (ngokubhala ngesandla).

Kuhlelo lwe-Cartesian coordinate (xyz) sisebenzisa i-unit vector u-i ukukhombisa isiqondiso se-x-axis esihle, u-j ukukhombisa isiqondiso se-y-axis esihle, u-k ukukhombisa isiqondiso se-y-axis esihle.

Izingxenye zeVektha

Ukuze kube lula ukuqonda, cabangela isibonelo esilandelayo. Isibonelo, kukhona i-vector F njengoba kuboniswe esithombeni esingezansi.

Esifanekisweni, i-vector yeyunithi i ikhombisa isiqondiso esihle se-x-axis kanye j ikhombisa isiqondiso esihle se-y-axis. Singasho ubudlelwano phakathi i-vector yengxenye kanye nezingxenye zazo, kanje:

F _x = F _x i

F _y = F _y j

Singabhala i-vector F ezingxenyeni zayo kanje:

F = F _x i + F _y j

Isibonelo, kunezivektha ezimbili, u-A no -B ohlelweni lwe-xy coordinate, lapho lezi zivektha ezimbili zivezwa ngokwezakhi zazo:

A = A _x i + A _y j

B = B _x i + B _y j

Kuthiwani uma u-A no -B behlanganiswa ndawonye?

R = A + B

R = ((A_xi + A_yj) + (B_xi + B_yj)

R = ((A_x + B_x)i + (A_y + B_y)j

R = R _x i + R _y j

Uma kungewona wonke amavektha akhona endizeni ye-xy khona-ke singangeza ivektha yeyunithi u-k, ekhombisa isiqondiso se-z-axis esihle.

A = A _x i + A _y j + A _z k

B = B _x i + B _y j + B _z k

Uma kungezwa amavekhtha u-A no -B , imiphumela elandelayo izotholakala:

R = A + B

R = ((A_xi + A_yj + A_zk) + (B_xi + B_yj + B_zk)

R = ((A_x + B_x)i + (A_y + B_y)j + (A_z + B_z)k

R = R _x i + R _y j + R _z k