Ngā Wāhanga Kino, Ngā Wāhanga Whakahē rānei: Te Ariā me te Whakamahinga i te Ao
He mea pāngarau te whārite, he rahi, he ahunga hoki tōna. Ka whakamahia ngā whārite i roto i ngā momo mara pūtaiao, pērā i te ahupūngao, te pāngarau, me te hangarau, hei tohu i ngā rahinga e hiahia ana kia nui atu i te uara tau anake. Ko tētahi ariā nui i roto i te ako i ngā whārite ko te whārite kino, te whārite ritenga kē rānei. Ka matapakihia e tēnei tuhinga te whakamāramatanga o te whārite kino, me pēhea te tatau, me tōna whakamahinga i roto i ngā momo āhuatanga o te oranga o ia rā.
Te Mārama ki ngā Wētera Kino
Ko te whārite kino, e mōhiotia ana ko te whārite ritenga kē, he whārite he rite te rahi engari he ritenga kē te ahunga ki te whārite taketake. Mena ko te whārite taketake e tohuhia ana e A , ko tōna whārite kino ka tohuhia i te nuinga o te wā e te tohu \(-\mathbf{A}\). Ara, ko ngā huānga o tēnei whārite he tohu ritenga kē ki ngā huānga o te whārite taketake.
I roto i te pāngarau, mēnā ko \(\mathbf{A} = (a_1, a_2, \ldots, a_n)\), ko te whārite kino ko \(-\mathbf{A} = (-a_1, -a_2, \ldots, -a_n)\). Ko te tikanga o tēnei ka hurihia ia wāhanga o te whārite taketake i roto i ngā taunga Cartesian ki te tohu ritenga i roto i te whārite kino.
Me pēhea te tatau i ngā whārite kino
He tino māmā te whakatau i tētahi whārite kino. Hei tauira, i roto i te wāhi rua-ahu (2D), mēnā kei a tātou te whārite \(\mathbf{A} = (3, 4)\), kātahi:
\[
-\mathbf{A} = (-3, -4)
\]
I roto i te wāhi ahu-toru (3D), mēnā ko \(\mathbf{A} = (2, -1, 5)\), kātahi:
\[
-\mathbf{A} = (-2, 1, -5)
\]
Kāore tēnei whakatau i ngā whārite tōraro e herea noa ki ngā whārite e rua, e toru rānei ngā ahu, engari ka taea te whakamahi ki ngā whārite he nui ake ngā ahu.
Ngā Whakamahinga o ngā Wāhitau Kino i roto i te Oranga o Ia Rā
He maha ngā whakamahinga o ngā whārite kino i roto i te ao tūturu i roto i te oranga o ia rā, me ngā momo marautanga. Anei ētahi tauira:
1. Ahupūngao me te Hangarau
I roto i te ahupūngao me te hangarau, he mea nui te ariā o ngā whārite kino i roto i te tātari i ngā kaha me te nekehanga. Hei tauira, i roto i te pūtaiao ā-pūmau me te hihiri, i te tatau i ngā kaha e pā ana ki tētahi mea, me whakaaro tātou ki ngā kaha i ngā ahunga rerekē hei whakatau i te pūwāhi taurite.
Ko tētahi atu tauira ko te rererangi me te whakatere. Ina tūtaki te waka rererangi ki te aueue, ki te rerekētanga o te huarahi, ki te rerekētanga rānei o te ahunga o te hau, me whakaaro te pailate ki te hau e anga atu ana ki te taha hei whakarerekē i te ara rere.
2. Ōhanga me te Pūtea
I roto i te ōhanga me te pūtea, ko ngā panonitanga o ngā utu, o ngā taupū rānei, ka tohuhia e ngā whārite. Hei tauira, ki te heke te utu hea o tēnei rā ki te utu o te rā o mua, ka taea te kī he whārite kino te panonitanga o te utu.
Ko te tātari whakarara, e whakamahia ana i roto i te ōhanga hei matapae i ngā au, ka taea hoki te whakaatu mā ngā whārite, ā, i ētahi wā, me whakaaro tātou ki ngā tauwehenga, ki ngā tauwehenga rānei kei te taha kē (ngā whārite kino) i roto i ā tātou tauira matapae.
3. Whakairoiro Rorohiko me te Pakiwaituhi
I roto i ngā whakairoiro rorohiko, ka whakamahia ngā whārite hei tautuhi i te tūranga, te aronga, me te nekehanga o ngā mea. Ka whakamahia ngā whārite tōraro hei mahi i ngā panonitanga pēnei i te whakaata me te whakahuri i te ahunga o te nekehanga pakiwaituhi.
Hei tauira, i te whakaata i tētahi mea 3D, ka taea e tātou te whakarea i ngā taunga o te mea ki tētahi wetereo kino hei whakaputa i te whakaata o taua mea ki runga i tētahi tuaka motuhake.
4. Te Matawhenua
I roto i te matawhenua, ka whakamahia te ariā o ngā whārite kino hei whakaahua i te nekehanga o ngā pereti tektonika, tae atu ki te ahunga o tō rātou nekehanga me te kaha o tō rātou pānga. Ka āwhina ēnei whārite i ngā tohunga matawhenua ki te mārama ki ngā whanaketanga o te Ao me te matapae i ngā kaupapa taiao pēnei i ngā rū whenua.
Ngā Tauira Take Tuturu
Hei whakamārama i te whakamahinga o ngā whārite kino, ka taea e tātou te titiro ki te tauira tūturu e whai ake nei i roto i te mara o te miihini:
Whakaarohia ngā kaha e rua e pā ana ki tētahi mea, ka huaina e tātou ko \(\mathbf{F_1}\) me \(\mathbf{F_2}\). Mēnā ka mahi ēnei kaha i te ahunga kotahi, ko te kaha katoa ko te tapeke o ngā kaha e rua:
\[
\mathbf{F_{tapeke}} = \mathbf{F_1} + \mathbf{F_2}
\]
Heoi, ki te mea kei te taha kē te kaha \(\mathbf{F_2}\) ki \(\mathbf{F_1}\), kāti:
\[
\mathbf{F_{tapeke}} = \mathbf{F_1} + (-\mathbf{F_2})
\]
Hei tauira, me kī kei ngā ahunga rerekē a \(\mathbf{F_1} = (10, 15)\) Newton me \(\mathbf{F_2} = (5, 7)\) Newton, kātahi:
\[
-\mathbf{F_2} = (-5, -7)
\]
Nō reira, ko te kaha katoa e pā ana ki te mea:
\[
\mathbf{F_{katoa}} = (10, 15) + (-5, -7) = (5, 8) \text{ Newton}
\]
Mai i tēnei tātaitanga, e mārama ana mā te tāpiri i ngā whārite kino o ngā kaha \(\mathbf{F_2}\), ka whiwhi tātou i te kaha katoa i runga i ngā ahunga rerekē, e ai ki te ariā o te whārite kino.
Whakamutunga
Ko ngā whārite tōraro, ngā whārite whakahē rānei, he ariā taketake i roto i te ako i ngā whārite, ā, he whānuitia te whakamahinga i roto i ngā momo mara pūtaiao me te oranga o ia rā. Mā te mārama ki te tautuhi me te whakamahi i ngā whārite tōraro, ka taea e tātou te whakahaere me te whakaoti rapanga uaua maha e hiahia ana kia tātarihia te ahunga me te rahi.
Mā te mōhio ki te tatau me te whakamahi i ngā whārite kino ka taea e tātou te whiwhi māramatanga whānui ake ki ngā kaupapa pēnei i te ahupūngao, te hangarau, te ōhanga, te whakairoiro rorohiko, me te whenua. Ehara i te mea he taputapu pāngarau noa iho ngā whārite kino, engari he mea nui hoki ki te whakaoti rapanga o te ao tūturu e uru ana ki te tātari whānui i te ahunga me te rahi.
