Mibvunzo yeMienzaniso neKukurukurirana kweKubvisa Vector
Pendauluan
Mumasvomhu nefizikisi, mavector ipfungwa huru inoshandiswa kutsanangura zviitiko zvakawanda zvechisikigo uye zveinjiniya. Vector huwandu hune hukuru uye gwara. Mimwe mienzaniso yakakosha yemavectors idisplacement, velocity, acceleration, uye force. Muchinyorwa chino, tichakurukura nezvekubvisa mavector, kunyangwe nyaya iyi ichinyanya kusimbiswa mukubatana kwemavector.
Kubvisa mavector ibasa guru rinokosha mukuongorora mavector. Kuti tinyatsonzwisisa pfungwa iyi, ngationgororei mimwe mienzaniso yezvinetso nehurukuro dzine chekuita nekubvisa mavector.
Kubvisa Vector
Kubvisa vhekitari {\displaystyle \mathbf{A} – \mathbf{B}} kunotsanangurwa sekushanda kwekuwedzera vhekitari {\displaystyle \mathbf{A}} nevekitari {\displaystyle -\mathbf{B}}, apo {\displaystyle -\mathbf{B}} iri vhekitari ine hukuru hwakafanana ne {\displaystyle \mathbf{B}} asi ine divi rakapesana. Pamasvomhu, izvi zvinogona kunyorwa seizvi:
{\ kuratidza style \ mathbf{A} - \ mathbf{B} = \ mathbf{A} + (-\ mathbf{B})}
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Kubvisa Mavekitari Ane Madhigirii Maviri
Ngatitii kune mavector maviri muCartesian coordinates:
{\displaystyle \mathbf{A} = (4, 3)} uye {\displaystyle \mathbf{B} = (1, 2)}. Verenga {\displaystyle \mathbf{A} – \mathbf{B}}.
Kukurukurirana:
Danho rekutanga nderekutsvaga vhekitari isina kunaka ye {\displaystyle \mathbf{B}}, inoti:
{\displaystyle -\mathbf{B} = (-1, -2)}
Tevere, wedzera vhekita {\displaystyle \mathbf{A}} ne {\displaystyle -\mathbf{B}}:
{\ showstyle \ mathbf{A} – \ mathbf{B} = (4, 3) + (-1, -2)}
Wedzera vhekita nekuwedzera chikamu chimwe nechimwe che x ne y:
{\ showstyle \ mathbf{A} – \ mathbf{B} = (4 + (-1), 3 + (-2))}
{\ showstyle \ mathbf{A} - \ mathbf{B} = (3, 1)}
Saka, mhedzisiro yekubvisa mavector {\displaystyle \mathbf{A} – \mathbf{B}} ndiyo vector (3, 1).
Mubvunzo 2: Kubvisa Maveki ane mativi matatu
Zvichipiwa mavector maviri muzvikamu zvitatu zvemakoordinates:
{\displaystyle \mathbf{P} = (2, -4, 6)} uye {\displaystyle \mathbf{Q} = (-3, 5, 7)}. Verenga {\displaystyle \mathbf{P} – \mathbf{Q}}.
Kukurukurirana:
Danho rekutanga nderekutsvaga vhekitari isina kunaka ye {\displaystyle \mathbf{Q}}:
{\displaystyle -\mathbf{Q} = (3, -5, -7)}
Tevere, wedzera vhekitari {\displaystyle \mathbf{P}} ne {\displaystyle -\mathbf{Q}}:
{\ kuratidza style \ mathbf{P} – \ mathbf{Q} = (2, -4, 6) + (3, -5, -7)}
Wedzera vhekita nekuwedzera chikamu chimwe nechimwe che x, y, uye z:
{\ showstyle \ mathbf{P} – \ mathbf{Q} = (2 + 3, -4 + (-5), 6 + (-7))}
{\ showstyle \ mathbf{P} - \ mathbf{Q} = (5, -9, -1)}
Saka, mhedzisiro yekubvisa mavector {\displaystyle \mathbf{P} – \mathbf{Q}} ndiyo vector (5, -9, -1).
Mubvunzo 3: Kubvisa Vector muComplex Plane
Ngatitii pane mavector maviri anomiririrwa nenhamba dzakaoma:
{\displaystyle \mathbf{M} = 3 + 4i} uye {\displaystyle \mathbf{N} = 1 + 2i}. Verenga {\displaystyle \mathbf{M} – \mathbf{N}}.
Kukurukurirana:
Danho rekutanga nderekutsvaga vhekitari isina kunaka ye {\displaystyle \mathbf{N}}:
{\ showstyle -\ mathbf{N} = -1 - 2i}
Tevere, wedzera vhekitari {\displaystyle \mathbf{M}} ne {\displaystyle -\mathbf{N}}:
{\ kuratidza style \ mathbf{M} – \ mathbf{N} = (3 + 4i) + (-1 – 2i)}
Wedzera vhekita nekuwedzera chikamu chimwe nechimwe chaicho uye chekufungidzira:
{\ showstyle \ mathbf{M} – \ mathbf{N} = (3 + (-1)) + (4i + (-2i))}
{\ showstyle \ mathbf{M} - \ mathbf{N} = 2 + 2i}
Saka, mhedzisiro yekubvisa mavector {\displaystyle \mathbf{M} – \mathbf{N}} ndiyo nhamba yakaoma 2 + 2i.
Mubvunzo 4: Kubvisa Vector muPolar Coordinate System
Ngatitii kune mavector maviri mu polar coordinates:
{\displaystyle \mathbf{U}} ine hukuru hwe5 uye kona ye30°,
uye {\displaystyle \mathbf{V}} ine hukuru hwe3 uye kona ye150°.
Verenga {\displaystyle \mathbf{U} – \mathbf{V}}.
Kukurukurirana:
Danho rekutanga nderekushandura mavector {\displaystyle \mathbf{U}} uye {\displaystyle \mathbf{V}} kuita maCartesian coordinates.
Zve{\ displaystyle \ mathbf{U}}:
{\displaystyle U_x = 5 \cos(30^\circ) = 5 \left(\frac{\sqrt{3}}{2}\right) = 5 \cdot 0.866 = 4.33}
{\displaystyle U_y = 5 \sin(30^\circ) = 5 \left(\frac{1}{2}\right) = 5 \cdot 0.5 = 2.5}
Saka {\displaystyle \mathbf{U}} muCartesian ndi (4.33, 2.5).
Zve{\ displaystyle \ mathbf{V}}:
{\displaystyle V_x = 3 \cos(150^\circ) = 3 \left(\frac{-\sqrt{3}}{2}\right) = 3 \cdot (-0.866) = -2.598}
{\displaystyle V_y = 3 \sin(150^\circ) = 3 \left(\frac{1}{2}\right) = 3 \cdot 0.5 = 1.5}
Saka {\displaystyle \mathbf{V}} muCartesian ndi (-2.598, 1.5).
Danho rinotevera, verenga kubvisa vhekitari muCartesian:
{\displaystyle \mathbf{U} – \mathbf{V} = (4.33, 2.5) – (-2.598, 1.5)}
Zvinoreva nekuwedzera negative yevector:
{\displaystyle \mathbf{U} – \mathbf{V} = (4.33 + 2.598, 2.5 – 1.5)}
{\displaystyle \mathbf{U} – \mathbf{V} = (6.928, 1)}
Saka, mhedzisiro yekubvisa vector {\displaystyle \mathbf{U} – \mathbf{V}} muCartesian coordinates ndeye (6.928, 1).
Mhedziso
Kubvisa mavector inzira yakakosha yemasvomhu muminda yakawanda inoshandisa kuongorora mavector. Ingava mumasystem e-dimensional maviri, three-dimensional, complex, kana polar coordinate, musimboti wekutanga unoramba wakafanana: kuwedzera vector imwe kune negative yeimwe. Mienzaniso iri pamusoro inoratidza nzira dzakasiyana dzekushandisa operation iyi mumamiriro akasiyana, zvichitibatsira kunzwisisa pfungwa yacho zvakadzama uye nemazvo.
