Procjena znanja

Povežite vektore zadane početnom i završnom točkom s radijvektorom.

Pridružite vektore njihovu prikazu u koordinatnoj ravnini.

$\stackrel{\to }{a}=3\stackrel{\to }{i}+3\stackrel{\to }{j}$

$\stackrel{\to }{b}=4\stackrel{\to }{j}$

$\stackrel{\to }{c}=4\stackrel{\to }{i}$

$\stackrel{\to }{d}=-2\stackrel{\to }{i}+4\stackrel{\to }{j}$

Zadani su vektori: $\stackrel{\to }{a}=\frac{3}{4}\stackrel{\to }{i}+7\stackrel{\to }{j},$ $\stackrel{\to }{b}=-\stackrel{\to }{i}+\stackrel{\to }{j}$ i $\stackrel{\to }{c}=\frac{2}{5}\stackrel{\to }{j}.$ Izračunajte: $2\stackrel{\to }{a}-\stackrel{\to }{b}+\stackrel{\to .}{c}$

Duljina vektora $2\stackrel{\to }{a}-3\stackrel{\to }{b}$ ako su zadani ovako: $\stackrel{\to }{a}=-\stackrel{\to }{i}-\stackrel{\to }{j}$ i $\stackrel{\to }{b}=-\stackrel{\to }{i}-\stackrel{\to }{j},$ jednaka je $\sqrt{2}.$

Spojite vektore s njihovim skalarnim umnošcima.

Zadani su vektori: $\stackrel{\to }{AB}=2\stackrel{\to }{i}-\stackrel{\to }{j}$ i $\stackrel{\to }{AC}=5\stackrel{\to }{j}.$ Za kut između vektora vrijedi:

Zadani su vektori: $\stackrel{\to }{a}=2\stackrel{\to }{i}+4\stackrel{\to }{j},$ $\stackrel{\to }{b}=-\stackrel{\to }{i}-3\stackrel{\to }{j}$ i $\stackrel{\to }{c}=2\stackrel{\to }{i}-5\stackrel{\to }{j}.$ Ako vektor $\stackrel{\to }{c}$ prikažemo kao linearnu kombinaciju vektora $\stackrel{\to }{a}$ i $\stackrel{\to }{b},$ koeficijent $\beta$ jednak je: