Vector hoʻokahi

Ke Hoʻomaopopo nei i nā Vectors Unit 

ʻO ka vector unit he vector nona ka nui he 1. ʻAʻohe unit o ka vector unit a lawelawe ia e hōʻike i kahi kuhikuhi ma ka lewa. No ka hoʻokaʻawale ʻana iā ia mai kahi vector maʻamau, ua paʻi ʻia me ka wiwo ʻole (no ka kikokikona i paʻi ʻia) a i ʻole ua hoʻokomo ʻia kahi hōʻailona ^ ma luna ona (no ke kākau lima ʻana).

Ma ka ʻōnaehana hoʻonohonoho Cartesian (xyz) hoʻohana mākou i ka vector unit i e hōʻike i ke kuhikuhi o ke axis-x maikaʻi, ʻo j e hōʻike i ke kuhikuhi o ke axis-y maikaʻi, ʻo k e hōʻike i ke kuhikuhi o ke axis-y maikaʻi.

Nā ʻĀpana Vector

I mea e maʻalahi ai ke hoʻomaopopo ʻana, e noʻonoʻo i kēia laʻana. Eia kekahi laʻana, aia kahi vector F e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo.

Ma ke kiʻi, ʻo ka vector unit i hōʻike i ke kuhikuhi axis-x maikaʻi a j hōʻike i ke kuhikuhi y-axis maikaʻi. Hiki iā mākou ke haʻi i ka pilina ma waena vector ʻāpana a me kā lākou mau ʻāpana, penei:

F _x = F _x i

Fy = Fyj_​​​

Hiki iā mākou ke kākau i ka vector F i loko o kona mau ʻāpana penei:

F = F _x i + F _y j

Eia kekahi laʻana, aia ʻelua mau vectors, ʻo A a me B i loko o ka ʻōnaehana hoʻonohonoho xy, kahi i hōʻike ʻia ai kēia mau vectors ʻelua ma ke ʻano o kā lākou mau ʻāpana:

A = A _x i + A _y j

B = B _x i + B _y j

A pehea hoʻi inā e hoʻohui ʻia ʻo A a me B ?

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

Inā ʻaʻole nā ​​vectors āpau ma ka mokulele xy a laila hiki iā mākou ke hoʻohui i kahi vector unit k, e hōʻike ana i ke kuhikuhi z-axis maikaʻi.

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

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

Inā hoʻohui ʻia nā vectors A a me B , e loaʻa nā hopena penei:

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