Lineárne kombinácia vektorov, ťažnice štvorstena
Dany je stvorsten ABCD zo suradnicami
A[2,4,1]
B[7,6,1]
C[4,1,1]
D[5,5,7]
Vektory:
u vektor = AB vektor
v vektor = AC vektor
w vektor = AD vektor
Zistite linearnu kombinaciu vektorov, ktore urcia vektory taznic vo vsetkych stenach stvorstena.
Este mam zadane pomocky, ze taznica
prva je medzi vektorom u a w
druha (spodna) je medzi u a v
a trietia je medzi v a w
Ja som to zacal riesit ze si urcim bod O (ktory je v strede medzi B a D), jeho suradnice (6, 11/2 , 4) potom: vektor t = AO vektor = O - A = (4, 3/2, -3)
u vektor = AB vektor = B -A = (5, 2, 0)
v vektor = AC vektor = C-A = (2, -3, 0)
w vektor = AD vektor = D -A = (3, 1, 6)
potom si dam
t vektor = k . u vektor + l . w vektor a z tohoto zapisu si spravim sustavu rovnic:
t1 = k . u1 + l . w1
t2= k . u2 + l . w2
t3 = k . u3 + l . w3
----------------
(potom dosadim cisla)
4 = 5k + 3l
3/2 = 2k + 1l
3 = 0k + 6l => l= 3/6 = 1/2
-----------------
(cize mam vypocitanu uz 1 neznamu som si vyjadril, idem zistit druhu cez prvu rovnicu)
4 = 5k + 3 * 1/2
4 = 5k + 3/2
5k =4 - 3/2
5k = 5/2
k= 1/2 (mam uz aj druhu neznamu)
a teraz si zoberiem druhy riadok sustavy rovnic a zistim ci sa rovna (ak ano tak je to linearna kombinacia) cize dosadim
3/2 = 2 * 1/2 + 1/2
3/2 = 2/2 + 1/2
3/2 = 3/2 => z coho vyplyva ze vektor t je linearnou kombinaciu vektorov u a v
Ale este to potrebujem spravit pre tie dalsie 2 vektory, lenze neviem ako si ich mam nactrnut (resp kde mam hladat bod O medzi ktorymi suradnicami) https://prnt.sc/2pxg6pveeZtz
Are you looking for matematika tutoring? Find the right matematika tutor for online or in-person tutoring near you.
We access the information stored on your device for this website to function properly. This includes, for example, cookies or local browser cache. We use this to store the data necessary for the functioning of the website, data used for analytical purposes, or data stored by third parties.
If this information is essential for the operation of this website, we store it automatically. For everything else, we need your consent, which you can choose to give below. Your consent is valid for 12 months. Should you refuse, we will ask you for consent again in 6 months, but you are free to change your mind at any time. For more information, please see our GDPR and Terms of Use.