Chitsanzo cha Mavuto Okambirana za Ma Vector Otsutsana
Vekitala ndi chinthu cha masamu chomwe chili ndi kukula ndi malangizo. Mu kuphunzira za mavekitala, nthawi zambiri timakumana ndi mavekitala okhala ndi makhalidwe enaake. Lingaliro limodzi lofunikira mu mavekitala ndi vekitala yotsutsana, kapena vekitala yotsutsa. Nkhaniyi ifotokoza zitsanzo ndi kukambirana za mavekitala otsutsana.
Kumvetsetsa Ma Vector Otsutsana
Vekitala yotsutsana, yomwe nthawi zambiri imatchedwa vekitala yotsutsa, ndi vekitala yomwe ili ndi kukula kofanana koma kosiyana ndi vekitala yoyambirira. Ngati vekitala ikuwonetsedwa ndi \(\vec{a}\), ndiye kuti vekitala yake yotsutsana ndi \(-\vec{a}\). Mwa masamu, ngati \(\vec{a} = (a_1, a_2, a_3)\), ndiye \(-\vec{a} = (-a_1, -a_2, -a_3)\).
Chitsanzo cha Funso 1
Popeza vekitala \(\vec{a} = (3, 4, -2)\). Dziwani vekitala yotsutsana ya \(\vec{a}\).
Kukambirana:
Kuti tidziwe vekitala yotsutsana ya \(\vec{a}\), timangofunika kusintha chilichonse mwa zigawo zake za vekitala kukhala negative:
\[
-\vec{a} = (-3, -4, 2)
\]
Kotero, vekitala yotsutsana ya \(\vec{a} = (3, 4, -2)\) ndi \(-\vec{a} = (-3, -4, 2)\).
Chitsanzo cha Funso 2
Lolani vekitala \(\vec{b} = (7, -5, 0)\). Pezani vekitala yotsutsana ya \(\vec{b}\) ndikutsimikizira kuti \(\vec{b} + (-\vec{b}) = \vec{0}\).
Kukambirana:
Choyamba, timafotokoza vekitala yotsutsana ya \(\vec{b}\):
\[
-\vec{b} = (-7, 5, 0)
\]
Kenako, tikutsimikiza kuti kuwonjezera kwa vekitala \(\vec{b}\) ndi vekitala yake yotsutsana kumabweretsa vekitala ya zero:
\[
\vec{b} + (-\vec{b}) = (7, -5, 0) + (-7, 5, 0)
\]
Timawonjezera zigawo za vekitala:
\[
(7 – 7, -5 + 5, 0 + 0) = (0, 0, 0)
\]
Kotero, \(\vec{b} + (-\vec{b}) = \vec{0}\), zatsimikiziridwa kuti zotsatira za kuwonjezera kwa vekitala \(\vec{b}\) ndi vekitala yake yotsutsana ndi zero vekitala.
Chitsanzo cha Funso 3
Popeza mavekitala \(\vec{u} = (2, -1)\) ndi \(\vec{v} = (-2, 1)\). Kodi \(\vec{u}\) ndiye vekitala yotsutsana ya \(\vec{v}\) ?
Kukambirana:
Kuti tidziwe ngati \(\vec{u}\) ndi \(\vec{v}\) ndi mavekitala otsutsana, tiyenera kuwona ngati \(\vec{v} = -\vec{u}\).
Werengerani \(-\vec{u}\):
\[
-\vec{u} = (-2, 1)
\]
Zikuoneka kuti \(-\vec{u} = \vec{v}\), izi zikutanthauza kuti vekitala \(\vec{u}\) ndiye vekitala yotsutsana ya vekitala \(\vec{v}\).
Chitsanzo cha Funso 4
Ngati vekitala \(\vec{w}\) imadziwika kuti ili ndi kukula kwa 5 ndi njira yotsutsana ndi vekitala \(\vec{p} = (4, 3)\), dziwani \(\vec{w}\) mu mawonekedwe a gawo.
Kukambirana:
Choyamba, timapeza kukula kwa vekitala \(\vec{p}\):
\[
|\vec{p}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5
\]
Popeza \(\vec{w}\) ili ndi kukula kofanana ndi \(\vec{p}\) koma mbali ina, ndiye kuti:
\[
\vec{w} = -\vec{p} = (-4, -3)
\]
Kotero, vekitala \(\vec{w}\) mu mawonekedwe a gawo ndi \(\vec{w} = (-4, -3)\).
Chitsanzo cha Funso 5
Mfundo A(2, 3) ndi mfundo B(4, 7) yoperekedwa. Dziwani vekitala ya malo kuchokera pa mfundo A kupita pa mfundo B ndi vekitala yomwe ili yosiyana ndi vekitala imeneyo.
Kukambirana:
Malo vekitala kuchokera pa mfundo A kupita pa mfundo B:
\[
\vec{AB} = (B_x – A_x, B_y – A_y) = (4 – 2, 7 – 3) = (2, 4)
\]
Vekitala yotsutsana ya \(\vec{AB}\):
\[
-\vec{AB} = (-2, -4)
\]
Kotero, vekitala yomwe ili yotsutsana ndi vekitala ya malo \(\vec{AB} = (2, 4)\) ndi \(-\vec{AB} = (-2, -4)\).
Chitsanzo cha Funso 6
Popeza vekitala \(\vec{m} = (x, y)\) ndipo vekitala yotsutsana ya \(\vec{m}\) ndi \( (-5, 12)\). Dziwani mtengo wa x ndi y.
Kukambirana:
Vekitala yotsutsana ya \(\vec{m}\) ndi \( (-x, -y) \), ndipo malinga ndi vuto, \((-x, -y) = (-5, 12)\).
Mwa kufananiza zigawo za vector, timapeza:
\[
-x = -5 \amatanthauza x = 5
\]
\[
-y = 12 \amatanthauza y = -12
\]
Kotero, mtengo wa \(x\) ndi 5 ndipo mtengo wa \(y\) ndi -12.
Mapeto
Mavekitala Otsutsana ndi mavekitala okhala ndi kukula kofanana koma kosiyana. Pomvetsetsa lingaliro la mavekitala otsutsana, titha kuthetsa mavuto osiyanasiyana okhudzana ndi mavekitala, monga kudziwa negative ya vekitala, kutsimikizira kuwonjezera mavekitala ku zero, ndi zina zotero. Kukambirana za mavuto omwe ali pamwambapa kukuyembekezeka kuwonjezera chidziwitso chathu ndi kumvetsetsa kwathu pakugwira ntchito ndi mavekitala otsutsana.
