Wetere Whakamuri
Pendahuluan
I roto i te pāngarau me te ahupūngao, he mea taketake te ariā o ngā whārite, ā, he maha ngā whakamahinga e whakamahia ana i roto i ngā momo tono, mai i te ahupūngao tawhito ki te tātari raraunga hou. Ko tētahi ariā whakamere i roto i te ako i ngā whārite ko te whārite whakamuri. Ka whakamāramahia e tēnei tuhinga he aha te whārite whakamuri, me pēhea te tatau, me ōna tono i roto i te oranga o ia rā me te pūtaiao.
He aha te Wetere?
I mua i te ruku hohonu ki te ariā o ngā whārite whakamuri, he mea nui kia mārama he aha te whārite. He mea pāngarau te whārite, he nui, he ahunga hoki tōna. Kāore i rite ki ngā tauine, he nui anake tōna, e rua ngā wāhanga matua o ngā whārite: te nui (te roa rānei) me te ahunga. Ko ngā whārite ka whakaaturia i te nuinga o te wā hei pere i roto i te wāhi rua-ahu, toru-ahu rānei, ko te roa o te pere e tohu ana i tōna rahi, ā, ko te ahunga o te pere e tohu ana i tōna ahunga.
I roto i ngā tuhi pāngarau, ka tuhia ngā whārite ki te āhua \( \mathbf{v} = (v_1, v_2, …, v_n) \), ko \( v_1, v_2, …, v_n \) ngā wāhanga o te whārite i roto i tētahi pūtake motuhake.
Te Whakamāramatanga o te Wetere Whakamuri
Ko te whārite whakamuri he whārite e anga ke ana ki te whārite taketake, engari he rite tonu te rahi. Mēnā he whārite tā tātou \( \mathbf{v} \), ko tōna whārite whakamuri ko \( -\mathbf{v} \).
Mehemea ko \( \mathbf{v} = (v_1, v_2, …, v_n) \), ko te whārite whakamuri ko \( -\mathbf{v} = (-v_1, -v_2, …, -v_n) \).
Hei tauira, mēnā ko \( \mathbf{v} = (3, 4) \), ko te whārite whakamuri ko \( -\mathbf{v} = (-3, -4) \).
Ngā Āhuatanga o ngā Wēka Whakamuri
Ko ētahi o ngā āhuatanga nui o ngā whārite whakamuri ko:
1. Ōrite Nui: He ōrite te rahi o te vector me tōna kōaroaro. Mena ko \( \|\mathbf{v}\| \) te rahinga o te vector \( \mathbf{v} \), ka \( \|-\mathbf{v}\| = \|\mathbf{v}\| \).
2. Tāpiri Kore: Mā te tāpiri i tētahi whārite me tōna whakamuri ka puta te whārite kore. Arā, \( \mathbf{v} + (-\mathbf{v}) = \mathbf{0} \).
3. Aronga Whakahē: He rerekē te ahunga o te whārite whakahē ki te whārite taketake. Mena ka tohu te whārite \( \mathbf{v} \) ki te raki, ka tohu te \( -\mathbf{v} \) ki te tonga.
Me pēhea te tatau i ngā whārite whakamuri
He tino māmā te tatau i te whārite whakamuri. Me kī he whārite tā tātou \( \mathbf{v} = (v_1, v_2, …, v_n) \). Hei kimi i tōna whārite whakamuri, me whakarerekē noa i te tohu o ia wāhanga:
\[ -\mathbf{v} = (-v_1, -v_2, …, -v_n) \]
Hei tauira, mēnā ko \( \mathbf{v} = (5, -3, 2) \), ko te whārite whakamuri ko \( -\mathbf{v} = (-5, 3, -2) \).
Ngā Taupānga Wētera Whakamuri
He maha ngā whakamahinga o te ariā o ngā whārite whakamuri i roto i ngā momo mara. Anei ētahi tauira:
1. Ahupūngao
I roto i te ahupūngao, he maha ngā wā ka whakamahia ngā whārite whakamuri hei whakaahua i ngā kaha, i ngā whakaterenga rānei e taupatupatu ana. Hei tauira, i roto i te tātaritanga o te nekehanga, mēnā kei te neke tetahi mea i tētahi ahunga, ka rerekē te ahunga o te kaha waku e pā ana ki te mea i te ahunga o te nekehanga. He whārite whakamuri anō hoki tō te whārite whakaterenga nā te kaha ā-papa e pā ana ki tētahi mea e hinga noa ana mēnā ka whakaarohia he pai te ahunga whakamuri.
2. Whakatere me te Robotics
I roto i te whakatere, ka whakamahia te whārite whakamuri hei tatau i te ara hoki. Hei tauira, ki te neke tētahi karetao, waka rānei mai i te pūwāhi A ki te pūwāhi B me tētahi whārite, hei hoki ki te pūwāhi A, me neke tahi me te whārite rerekē mai i te whārite i whakamahia hei haere ki te pūwāhi B.
3. Whakairoiro Rorohiko
I roto i ngā whakairoiro rorohiko, ka whakamahia ngā whārite whakamuri mō ngā mahi whakamārama me te whakamarumaru. Mena ka ahu mai te pūtake mārama i tētahi ahunga, ka whakamahia te whārite whakamuri o taua ahunga hei tatau i ngā atarangi me ngā whakaata i runga i te mata o te mea.
4. Tātari Raraunga
I roto i te tātari raraunga, ka whakamahia ngā whārite whakamuri i roto i ngā momo rauropi arotau. Hei tauira, i roto i te hekenga whakarara, hei whakaiti i tētahi mahi, ka neke tātou i te ahunga kino o te whakarara o taua mahi, arā, te whārite whakamuri o te whakarara.
Whakamutunga
He ariā māmā engari he tino whai hua ngā whārite whakamuri i roto i te whānuitanga o ngā tono pāngarau me te pūtaiao. Mā te mārama ki te tatau me te whakamahi i ngā whārite whakamuri, ka taea e tātou te tātari me te whakaoti rapanga i roto i te ahupūngao, te whakatere, te whakairoiro rorohiko, me te tātari raraunga.
Mā te mārama pai ki ngā whārite me ō rātou whakamuri ka huaki ake ngā huarahi maha mō te whakaoti rapanga o te ao tūturu me te whakawhanake i ngā hangarau hou. Pērā i te maha o ngā ariā o te pāngarau, ko te ataahua me te whai huatanga o ngā whakamuri whārite kei roto i tō rātou tino māmā me te whānui o ngā tono.
