1.1.10 Vector Algebra

Problem: Are the vectors \( \overrightarrow{c_{1}} \) and \( \overrightarrow{c_{2}} \), constructed from the vectors \( \vec{a} \) and \( \vec{b} \) collinear? \[ \begin{array}{l} \vec{a}=\{-2 ; 7 ;-1\}, \quad \vec{b}=\{-3 ; 5 ; 2\}, \\ \overrightarrow{c_{1}}=2 \vec{a}+3 \vec{b}, \quad \overrightarrow{c_{2}}=3 \vec{a}+2 \vec{b} . \end{array} \]