Li-Vector tsa Maemo: Metheo, Litšebeliso, le Mehlala Bophelong ba Letsatsi le Letsatsi
Pendahuluan
Vekthara ea boemo ke mohopolo oa bohlokoa lipalo le fisiks o sebelisoang ho hlalosa boemo ba ntlha sebakeng. Ka mantsoe a bonolo, vekthara ea boemo e ka nahanoa e le motsu o supang ho tloha qalong (hangata tšimoloho) ho ea ntlheng e itseng. Sehlooho sena se tla tšohla tlhaloso ea vekthara ea boemo, likarolo tsa eona, mokhoa oa ho e bala, le ts'ebeliso ea eona e sebetsang bophelong ba letsatsi le letsatsi.
Tlhaloso ea Vektara ea Boemo
Vekthara ea boemo ke vekthara e hokahanyang tšimoloho le ntlha sebakeng. Ha ho sebetsa sebakeng sa mahlakore a mabeli (2D), vekthara ea boemo e hlahisoa e le para e laetsoeng \((x, y)\), moo \(x\) le \(y\) e leng likhokahano tsa ntlha. Sebakeng sa mahlakore a mararo (3D), vekthara ea boemo e hlahisoa e le triplet e laetsoeng \((x, y, z)\).
Mohlala, haeba re na le ntlha A ho di-coordinates (3, 4) sebakeng sa 2D, jwale vekthara ya boemo e hokahanyang tshimoloho (0,0) le ntlha A ke \(\mathbf{r} = 3\mathbf{i} + 4\mathbf{j}\), moo \(\mathbf{i}\) le \(\mathbf{j}\) e leng divekthara tsa yuniti ho latela di-axes tsa \(x\) le \(y\).
Likarolo tsa Vektheri ea Boemo
Vekthara ea boemo e na le likarolo tse emelang libaka tse hokahaneng le li-axes tsa coordinate. Sebakeng sa 2D, vekthara ea boemo \(\mathbf{r}\) e ka hlalosoa ka tsela ena:
\[
\mathbf{r} = x\mathbf{i} + y\mathbf{j}
\]
Mona, \(x\) ke karolo ea vekthara ea boemo ho latela motsoako oa \(x\), 'me \(y\) ke karolo ea vekthara ea boemo ho latela motsoako oa \(y\).
Sebakeng sa 3D, vekthara ea boemo \(\mathbf{r}\) e hlahisoa ka tsela ena:
\[
\mathbf{r} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}
\]
Mona, \(x\), \(y\), le \(z\) ke dikarolo tsa vekthara ya boemo ho latela dilepe tsa \(x\), \(y\), le \(z\), ka ho latellana, ha \(\mathbf{k}\) e le vekthara ya yuniti ho latela mothapo wa \(z\).
Mokhoa oa ho Bala Vector ea Boemo
Ho bala vektara ya boemo ho kenyelletsa ho fumana sebaka ho tloha tshimolohong ho ya ntlheng e botswang ho di-coordinate tsa Cartesian. Mohlala, haeba ntlha ya B e le ho di-coordinate (5, 7) sebakeng sa 2D, vektara ya boemo e hokahanyang tshimoloho (0, 0) le ntlha ya B ke:
\[
\mathbf{r_B} = 5\mathbf{i} + 7\mathbf{j}
\]
Ho bala bolelele ba vektara ya boemo (kapa boholo), re sebedisa theorem ya Pythagorean. Bolelele ba vektara ya boemo \(\mathbf{r}\) sebakeng sa 2D bo fanwa ke:
\[
|\mathbf{r}| = \sqrt{x^2 + y^2}
\]
Sebakeng sa 3D, bolelele ba vekthara ea boemo \(\mathbf{r}\) bo baloa ka tsela ena:
\[
|\mathbf{r}| = \sqrt{x^2 + y^2 + z^2}
\]
Mohlala, bakeng sa ntlha C ho likhokahano (3, 4, 5) sebakeng sa 3D, bolelele ba vekthara ea boemo \(\mathbf{r_C}\) ke:
\[
|\mathbf{r_C}| = \sqrt{3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} \hoo e ka bang 7.07
\]
Litšebeliso tsa Li-Vector tsa Boemo Bophelong ba Letsatsi le Letsatsi
Li-vector tsa maemo li na le lits'ebetso tse ngata tse sebetsang masimong a fapaneng. Mehlala e meng ea ts'ebeliso ea tsona bophelong ba letsatsi le letsatsi ke ena:
1. Tsamaiso le GPS
Litsamaisong tsa ho tsamaya tse kang GPS, li-vector tsa boemo li sebelisoa ho fumana sebaka sa mosebelisi ha se bapisoa le lisathelaete tsa GPS. Lintlha tsena tsa boemo li sebelisoa ho bala sebaka le tataiso ea leeto.
2. Boenjiniere ba Meaho le Meaho
Baenjiniere ba tsa meaho le litsebi tsa meralo ba sebelisa li-vector tsa maemo ho rala meaho le meralo ea motheo. Li-vector tsena li thusa ho fumana maemo a amanang le likarolo tse fapaneng tsa meaho.
3. Bolepi ba linaleli
Thutong ea linaleli, li-vector tsa boemo li sebelisoa ho hlalosa maemo a linaleli, lipolanete le lintho tse ling tsa leholimo mabapi le Lefatše kapa setsi sa tsamaiso ea letsatsi.
4. 'Mele
Fisiks, li-vector tsa boemo li bohlokoa bakeng sa tlhahlobo ea motsamao. Mohlala, tlhahlobong ea motsamao oa projectile, li-vector tsa boemo li sebelisoa ho fumana boemo ba ntho ka linako tse fapaneng.
5. Liroboto
Lirobotong, li-vector tsa boemo li sebelisoa ho laola motsamao oa roboto. Li-vector tsena li thusa roboto ho fumana sebaka sa eona le tataiso ea motsamao.
Lipotso le Litharollo tsa Mehlala
Se latelang ke mohlala oa potso ho hlakisa kutloisiso ea li-vector tsa boemo.
Potso:
Ntlha ea P e ho likhokahano (2, 3) 'me ntlha ea Q e ho likhokahano (5, 7) sebakeng sa 2D. Fumana vekthara ea boemo e hokahanyang ntlha ea P le ntlha ea Q 'me u bale bolelele ba vekthara.
Tharollo:
Vekthara ea boemo \(\mathbf{PQ}\) ke ntlha e hokahanyang vekthara P ho ntlha Q. Re ka bala likarolo tsa vekthara \(\mathbf{PQ}\) ka ho tlosa likhokahano tsa P ho likhokahano tsa Q:
\[
\mathbf{PQ} = (5 – 2)\mathbf{i} + (7 – 3)\mathbf{j} = 3\mathbf{i} + 4\mathbf{j}
\]
Bolelele ba vekthara ya boemo \(\mathbf{PQ}\) ke:
\[
|\mathbf{PQ}| = \ sqrt{3^2 + 4^2} = \ sqrt{9 + 16} = \ sqrt{25} = 5
\]
Kahoo, ntlha e hokahanyang vekthara ya boemo P ho ntlha Q ke \(3\mathbf{i} + 4\mathbf{j}\) mme bolelele ba vekthara ke diyuniti tse 5.
Qetello
Vekthara ea boemo ke mohopolo oa motheo o sebelisoang ho hlalosa sebaka sa ntlha sebakeng. Ho utloisisa likarolo le mokhoa oa ho bala vekthara ea boemo ho bohlokoa bakeng sa mefuta e mengata ea lits'ebetso tse sebetsang, ho tloha ho tsamaiseng ho ea ho tlhahlobo ea 'mele. Ho utloisisa metheo ena ho etsa hore ho be bonolo ho utloisisa le ho sebelisa mohopolo oa li-vekthara tsa boemo bophelong ba letsatsi le letsatsi le masimong a profeshenale.
