I am working on a question from the first chapter of a Linear Algebra textbook I'm reading.
Let $A=(1,1,-1)$, $B=(-3,2,-2)$, and $C=(2,2,-4)$. Prove that $\Delta ABC$ is a right-angled triangle.
I know that the angle between $\overrightarrow{AB}$ and $\overrightarrow{AC}$ must be $90°$. In other words, $\overrightarrow{AB} \cdot \overrightarrow{AC}=0$. My trouble is I cant translate these given points into vectors in order to show the necessary calculations. I'm having the same trouble with other questions. Any help would be appreciated.