Amavekhtha Anezinhlangothi Ezintathu Kuhlelo Lokuxhumanisa lweCartesian
I-Pendahuluan
I-vector yinto yezibalo enobukhulu kanye nesiqondiso. Empilweni yansuku zonke, ama-vector avame ukusetshenziswa ukumela izimo ezahlukahlukene zomzimba njengejubane, amandla, kanye nokufuduka. Kuhlelo lwe-Cartesian coordinate olunezinhlangothi ezintathu, i-vector imelelwa yizingxenye ezintathu ezihlobene nama-axes ka-x, y, kanye no-z. Lesi sihloko sizoxoxa ngemibono eyisisekelo yama-vector ohlelweni lwe-Cartesian coordinate olunezinhlangothi ezintathu, imisebenzi eyisisekelo kuma-vector, kanye nezinye zezinhlelo zawo ezisebenzayo.
Uhlelo Lokuxhumanisa Lwe-Cartesian Olunezinhlangothi Ezintathu
Uhlelo lwe-Cartesian coordinate olunezinhlangothi ezintathu luqukethe ama-axe amathathu aqonde komunye nomunye, okungukuthi ama-axes ka-x, y, kanye no-z. Imvelaphi (0,0,0) yindawo lapho la ma-axes amathathu ehlangana khona. Iphuzu ngalinye esikhaleni esinobukhulu obuthathu lingamelwa njenge-triplet (x, y, z), lapho u-x eyi-coordinate ku-x-axis, u-y eyi-coordinate ku-y-axis, kanti u-z uyi-coordinate ku-z-axis.
Ukumelwa kweVektha
Ivektha esikhaleni esinezinhlangothi ezintathu ivame ukumelwa njenge-\(\mathbf{v} = \langle v_x, v_y, v_z \rangle\), lapho i-\(v_x\), i-\(v_y\), kanye ne-\(v_z\) kuyizingxenye zevektha eceleni kwe-x, y, kanye ne-z axes. Isibonelo, ivektha \(\mathbf{a} = \langle 3, 4, 5 \rangle\) inezingxenye \(a_x = 3\), \(a_y = 4\), kanye ne-\(a_z = 5\).
Ubude beVektha
Ubude noma ubukhulu bevektha \(\mathbf{v}\) bungabalwa kusetshenziswa ifomula:
\[ \|\mathbf{v}\| = \sqrt{v_x^2 + v_y^2 + v_z^2} \]
Isibonelo, ku-vektha \(\mathbf{a} = \langle 3, 4, 5 \rangle\), ubude buyi:
\[ \|\mathbf{a}\| = \sqrt{3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2} \]
Imisebenzi Eyisisekelo Kuma-Vector
Ukwengezwa Nokususwa Kwevekhtha
Ukwengeza amavekhtha amabili kwenziwa ngokungeza izingxenye zawo. Uma \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\) kanye \(\mathbf{b} = \langle b_x, b_y, b_z \rangle\), khona-ke:
\[ \mathbf{a} + \mathbf{b} = \inqe a_x + b_x, a_y + b_y, a_z + b_z \rangle \]
Ngokuphambene nalokho, ukunciphisa i-vector kwenziwa ngokususa izingxenye zayo:
\[ \mathbf{a} – \mathbf{b} = \ingle a_x – b_x, a_y – b_y, a_z – b_z \rangle \]
Ukuphindaphinda kwe-Scalar
Ukuphindaphinda kwevektha nge-scalar kwenziwa ngokuphindaphinda ingxenye ngayinye yevektha nge-scalar. Uma i-\(k\) iyi-scalar futhi i-\(\mathbf{a} = \langle a_x, a_y, a_z \rangle\), khona-ke:
\[ k \mathbf{a} = \LANGle k a_x, k a_y, k a_z \ingxabano \]
Ukuphindaphinda kwamavektha
Umkhiqizo we-Dot
Umkhiqizo wechashazi wamavekhtha amabili ukhiqiza umkhiqizo we-scalar futhi usetshenziselwa ukubala ukuthi amavekhtha amabili ahambisana kangakanani. Uma \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\) kanye \(\mathbf{b} = \langle b_x, b_y, b_z \rangle\), khona-ke:
\[ \mathbf{a} \cdot \mathbf{b} = a_x b_x + a_y b_y + a_z b_z \]
Umkhiqizo Ohlukile
Umkhiqizo ohlanganisiwe wamavektha amabili ukhiqiza ivektha entsha eqonde ngqo kumavektha womabili okuqala. Uma \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\) kanye \(\mathbf{b} = \langle b_x, b_y, b_z \rangle\), khona-ke:
\[ \mathbf{a} \izikhathi \mathbf{b} = \langle a_y b_z – a_z b_y, a_z b_x – a_x b_z, a_x b_y – a_y b_x \rangle \]
Ukusetshenziswa Kwama-Vector Empilweni Yansuku Zonke
Ifiziksi
Ku-physics, ama-vector asetshenziswa ukumela amanani ahlukahlukene, njengamandla, ijubane, kanye nomfutho. Isibonelo, amandla adonsela phansi asebenza entweni aqondiswa enkabeni yoMhlaba futhi ubukhulu bawo buxhomeke ebunzini bento kanye nebanga layo ukusuka enkabeni. Sisebenzisa ama-vector, singabala amandla avelayo asebenza entweni ethintwe amandla amaningi ngasikhathi sinye.
lobuchwepheshe
Kubunjiniyela, amavekhtha asetshenziswa ekuhlaziyweni kwesakhiwo kanye nobuchwepheshe bokukhanda ukuze kutholakale amandla asebenza esakhiweni noma emshinini. Onjiniyela basebenzisa amavekhtha ukuze babale ama-torque, ukucindezeleka, kanye nokuguquguquka okwenzeka ezintweni ezahlukene ngaphakathi kwesakhiwo.
Ihluzo Zekhompyutha
Kuma-computer graphics, ama-vector asetshenziswa ukumela indawo, isiqondiso, kanye nokunyakaza kwezinto esikhaleni esinezinhlangothi ezintathu. Ama-vector abalulekile ekuguqulweni kwejometri njengokujikeleza, ukuhumusha, kanye nokulinganisa. Ukusebenzisa ama-vector kungenza ama-animation kanye nokulingisa kwefiziksi kube ngokoqobo kakhudlwana.
Ukuzulazula
Ekuzulazuleni, amavekhtha asetshenziswa ukunquma isiqondiso kanye nebanga phakathi kwamaphuzu amabili. Izinhlelo zokuzulazula zesathelayithi ezifana ne-GPS zisebenzisa amavekhtha ukubala indawo kanye nomzila wemoto noma umkhumbi. Ngokusebenzisa lolu lwazi, umzila osheshayo noma omfushane ungatholakala.
Isiphetho
Amavekhtha anezinhlangothi ezintathu ohlelweni lwe-Cartesian coordinate angumqondo oyisisekelo osetshenziswa emikhakheni ehlukahlukene yesayensi nobuchwepheshe. Ngokuqonda izisekelo zamavekhtha, imisebenzi eyisisekelo angayenza, kanye nokusetshenziswa kwawo empilweni yansuku zonke, singasebenzisa lo mqondo ukuxazulula izinkinga ezahlukahlukene ezisebenzayo. Amavekhtha awagcini nje ngokwenza kube lula ukumelwa nokuhlaziywa kwezehlakalo ezibonakalayo kodwa futhi avula indlela yokusungula izinto ezintsha kanye nokuthuthukiswa kobuchwepheshe obusha nobuyinkimbinkimbi.
