Chav vector

Nkag Siab Txog Cov Vectors Hauv Chav 

Ib lub vector unit yog ib lub vector uas nws qhov loj yog 1. Ib lub vector unit tsis muaj units thiab ua haujlwm los qhia qhov kev taw qhia hauv qhov chaw. Txhawm rau kom paub qhov txawv ntawm ib lub vector ib txwm, nws raug luam tawm ua ntawv tuab (rau cov ntawv luam tawm) lossis ib lub cim ^ raug ntxig rau saum nws (rau kev sau ntawv).

Hauv Cartesian coordinate system (xyz) peb siv lub unit vector i los qhia qhov kev taw qhia ntawm x-axis zoo, j los qhia qhov kev taw qhia ntawm y-axis zoo, k los qhia qhov kev taw qhia ntawm y-axis zoo.

Cov Cheebtsam Vector

Yuav kom yooj yim to taub, xav txog cov piv txwv hauv qab no. Piv txwv li, muaj ib lub vector F raws li pom hauv daim duab hauv qab no.

Hauv daim duab, lub vector unit i qhia txog kev taw qhia x-axis zoo thiab j qhia txog qhov kev taw qhia y-axis zoo. Peb tuaj yeem hais txog kev sib raug zoo ntawm cov khoom sib xyaw vector thiab lawv cov khoom sib xws, raws li nram no:

Fx = Fx i_​​

F _y = F _y j

Peb tuaj yeem sau cov vector F hauv nws cov khoom raws li hauv qab no:

F = F _x i + F _y j

Piv txwv li, muaj ob lub vectors, A thiab B nyob rau hauv lub xy coordinate system, qhov twg ob lub vectors no tau qhia nyob rau hauv cov nqe lus ntawm lawv cov khoom:

A = A _x i + A _y j

B = B _x i + B _y j

Yog tias A thiab B raug ntxiv ua ke, yuav ua li cas?

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

Yog tias tsis yog txhua lub vectors nyob hauv lub dav hlau xy ces peb tuaj yeem ntxiv ib lub unit vector k, uas qhia txog qhov kev taw qhia zoo ntawm z-axis.

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

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

Yog tias ntxiv cov vectors A thiab B , cov txiaj ntsig hauv qab no yuav tau txais:

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