Dana sta vektorja $\overset{\rightharpoonup}{a},\overset{\rightharpoonup}{b}$ z dolžinama $|\overset{\rightharpoonup}{a}|=4,|\overset{\rightharpoonup}{b}|=2$, kot med njima pa meri $120^\circ$. Izračunaj tak $m$, da bosta vektorja $\overset{\rightharpoonup}{c}=\overset{\rightharpoonup}{a}+m\overset{\rightharpoonup}{b}$ in $\overset{\rightharpoonup}{d}=2\overset{\rightharpoonup}{a}-3\overset{\rightharpoonup}{b}$ pravokotna.

Ali za poljubne vektorje $\overset{\rightharpoonup}{a},\overset{\rightharpoonup}{b},\overset{\rightharpoonup}{c}$ velja enakost $$(\overset{\rightharpoonup}{a}\cdot\overset{\rightharpoonup}{b})\overset{\rightharpoonup}{c}=\overset{\rightharpoonup}{a}(\overset{\rightharpoonup}{b}\cdot \overset{\rightharpoonup}{c})?$$ Odgovor utemelji.

Dan je paralelogram $ABCD$ s stranicama $a=2,b=1$ in kotom $\alpha=60^\circ$. Izračunaj:

a) skalarni produkt $\overset{\Large\rightharpoonup}{AB}\cdot\overset{\Large\rightharpoonup}{AC}$,               b) dolžino vektorja $\overset{\Large\rightharpoonup}{AC}$,

c) na minuto natančno kot med vektorjema $\overset{\Large\rightharpoonup}{AB}$ in $\overset{\Large\rightharpoonup}{AC}$.