Ngā Wētera Taurite: Ngā Wētera Taurite
I roto i te pāngarau me te ahupūngao, he mea nui ngā whārite e whakamahia ana hei tohu i ngā rahinga me te rahi me te ahunga. Mai i ngā tono ngāwari pēnei i te whakatau i te tūranga i te wāhi ki ngā raupapa mahi uaua i roto i te whanaketanga wai, ka horapa te ariā o ngā whārite ki ngā peka pūtaiao maha. Ko tētahi ariā matua hei mārama ko ngā whārite ōrite, ko te whārite kotahi rānei.
Te Mārama ki ngā Wētere
I mua i tā tātou tūhuratanga hohonu atu ki te ariā o ngā whārite ōrite, me tīmata tātou mā te mārama he aha te whārite. Ko te whārite he mea pāngarau e tohuhia ana e te pere e rua ngā āhuatanga matua: te rahi (te roa rānei) me te ahunga. Hei tauira, ka taea te whakaatu i te kaha, te tere, me te papa hiko hei whārite.
Mā te pāngarau, ka taea te whakaatu i tētahi whārite i ngā taha e rua hei \((x, y)\), ko \(x\) me \(y\) ngā wāhanga o te whārite i runga i ngā tuaka \(x\) me \(y\). I roto i ngā taha e toru, ka whakaatuhia he whārite hei \((x, y, z)\.
Ngā Wētera Taurite
E kiia ana he ōrite, he rite rānei ngā whārite mēnā he ōrite te rahi me te ahunga. Ka rerekē pea ngā tūranga tīmatanga (hiku) me te tūranga whakamutunga (upoko), engari mēnā he ōrite te roa me te ahunga, ka kiia he ōrite. Hei tauira, e rua ngā whārite \(\vec{A} = (3, 4)\) me \(\vec{B} = (3, 4)\) i roto i ngā āhuatanga e rua, ka kiia he ōrite nā te mea he ōrite ō rāua wāhanga, ā, e tohu ana rāua i ngā whārite ōrite i runga i te roa me te ahunga.
Me pēhea te whakatau i ngā whārite ōrite
Hei whakatau mena he ōrite ngā pūwero e rua, ka taea e tātou te whai i ētahi mahi māmā:
1. Tirohia ngā Wāhanga:
Tirohia mēnā he ōrite ngā wāhanga \(x\) me \(y\) (\(z\) rānei i ngā taha e toru) o ngā whārite e rua. Mēnā he ōrite ēnei wāhanga, he ōrite ngā whārite.
2. Tirohia te Rahi:
Me rite te rahi o ngā whārite ōrite. Ka tatauhia te rahi o tētahi whārite \(\vec{A} = (x, y)\) i roto i ngā taha e rua mā te tātai:
\[
|\vec{A}| = \sqrt{x^2 + y^2}
\]
I roto i ngā āhuatanga e toru, ko te tātai koia tēnei:
\[
|\vec{A}| = \sqrt{x^2 + y^2 + z^2}
\]
3. Tirohia te Aronga:
Ahakoa he onge i roto i te horopaki o ngā whārite taketake, tera pea ētahi wā ka rerekē ngā ahunga o ngā whārite e rua engari he rite tonu te rahi. Heoi, e hono ana tēnei ki te ariā o te 'whārite kino', arā, he rerekē ngā ahunga engari he rite tonu ngā rahi.
Mā te whai i ēnei kaupae, ka taea e tātou te whakarite he ōrite ngā whārite e rua e whakatauritea ana e tātou.
Ngā Mahi me ngā Wekete Ōrite
Mā te mārama he ōrite ngā momo whārite rerekē ka taea e tātou te whakahaere i ngā mahi pāngarau. Anei ētahi mahi whārite taketake me ō rātou pānga ki ngā whārite ōrite:
1. Tāpiritanga Wētera:
Ka mahia te tāpiritanga whārite mā te tāpiri i ō rātou wāhanga e rite ana. Mena ko \(\vec{A} = (x_1, y_1)\) me \(\vec{B} = (x_2, y_2)\), ko te hua o te tāpiritanga ko:
\[
\vec{A} + \vec{B} = (x_1 + x_2, y_1 + y_2)
\]
Ka pā anō hoki tēnei ki ngā whārite ōrite; ki te ōrite ngā whārite e rua i mua i te tāpiritanga, ka ōrite tonu ngā hua.
2. Te Tangohanga Wetereo:
He tino rite te mahi tango ki te mahi tāpiri, arā, ka tangohia ngā wāhanga e tika ana:
\[
\vec{A} – \vec{B} = (x_1 – x_2, y_1 – y_2)
\]
3. Whakarea Tauine:
Ina whakareatia he whārite \(\vec{A}\) ki te tauine \(k\), ko te hua koia tēnei:
\[
k \vec{A} = (kx, ky)
\]
Ka puta he whārite he ōrite te tauine me te ahunga i roto i te panoni tauine i roto i tētahi whārite ōrite.
Ngā Tauira o te Ao Tūturu
He tino whai hua te ariā o ngā whārite ōrite i roto i ngā momo tono o te ao tūturu. Hei tauira, i roto i te ahupūngao, ka taea te whakaatu i ngā kaha e pā ana ki tētahi mea mā ngā whārite. Ahakoa he rerekē te wāhi e mahi ana ngā kaha e rua, ka rite tonu te pānga ki te nekehanga o te mea.
Waihoki, i roto i te pūtaiao rorohiko me ngā whakairoiro rorohiko, ka whakamahia ngā whārite hei tohu i te tūranga me ngā huringa o te wāhi. Ko ngā tikanga e whakawhirinaki ana ki ngā huringa whārite e whakaaro pinepine ana ka taea te whakakapi i ngā whārite ōrite tetahi ki tetahi me te kore e whakarerekē i te hua whakamutunga.
Whakamutunga
He mea nui te mārama ki te ariā o ngā whārite ōrite, te whārite ōrite rānei, ki ngā kaupapa pūtaiao maha. He ōrite ngā whārite e rua mēnā he ōrite te rahi me te ahunga, ahakoa te tīmatanga, te mutunga rānei. Mā te mōhio me te tūhura i tēnei ariā ka māmā ake ngā mahi pāngarau, te tātari ā-tinana, me ngā tono i roto i te hangarau.
Mā tēnei māramatanga, ehara i te mea ka ako noa tātou i ngā tataunga pāngarau engari ka hohonu ake hoki te māramatanga ki te pānga o ngā whakaaturanga whārite ki te tātari me te whakaoti rapanga o te ao tūturu. Ko te mōhiotanga ki ngā whārite ōrite he tūāpapa hei whakakaha i te tūāpapa pāngarau, ā, he whānui, he kanorau hoki te whakamahinga i roto i ngā momo marautanga.
