Volumen paralelopipeda

Izračunajte volumen paralelopipeda razapetog vektorima

$\displaystyle \mathbf{a}=\mathbf{i}-3\mathbf{j}+\mathbf{k},\qquad \mathbf{b}=2\... ...i}+\mathbf{j}-3\mathbf{k}, \quad \mathbf{c}=\mathbf{i}+2\mathbf{j}+ \mathbf{k}.$

Rješenje. Prema [M1, poglavlje 3.11], volumen zadanog paralelopipeda iznosi

$\displaystyle V=\vert(\mathbf{a}\times\mathbf{b})\cdot \mathbf{c}\vert=\vert\be... ...1 & 2 & 1\end{vmatrix} \vert=\vert 1\cdot(1+6)+3\cdot(2+3)+1\cdot(4-1)\vert=25.$