Dane su točke \(A\left( -3,4\right) ,B\left( 2,-1\right) ,C\left(3,0\right) .\) Odredi vektore \(\overrightarrow{AB},\overrightarrow{BC}\:i\:\overrightarrow{CA}\) te provjeri da je \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=\overrightarrow{0}\).

Prikaze traženih vektora su:

\[\begin{gather*}\overrightarrow{AB} =\left(2+3\right)\overrightarrow{i}+\left(-1-4\right)\overrightarrow{j}=5\overrightarrow{i}-5\overrightarrow{j}\\ \overrightarrow{BC} =\left(3-2\right)\overrightarrow{i}+\left(0+1\right)\overrightarrow{j}=\overrightarrow{i}+\overrightarrow{j}\\ \overrightarrow{CA} =\left(-3-3\right)\overrightarrow{i}+\left(4-0\right)\overrightarrow{j}=-6\overrightarrow{i}+4\overrightarrow{j}\end{gather*}\]

Zbroj ovih vektora je

\[\begin{equation*}\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA} =5\overrightarrow{i}-5\overrightarrow{j}+\overrightarrow{i}+\overrightarrow{j}-6\overrightarrow{i}+4\overrightarrow{j}=\overrightarrow{0} \end{equation*}\]