Answer:
[tex]\boxed{\textbf{a}-\dfrac{3}{2}\textbf{b}}[/tex]
[tex]\boxed{10 \textbf{a}-15\textbf{b}}[/tex]
[tex]\boxed{-4 \textbf{a}+6\textbf{b}}[/tex]
[tex]\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}[/tex]
Step-by-step explanation:
Given vector:
[tex]\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}[/tex]
Two vectors are parallel if one can be written as a scalar multiple of the other.
Therefore, the following vectors are parallel to FG:
[tex]\textbf{a}-\dfrac{3}{2}\textbf{b}=\dfrac{1}{2}(2 \textbf{a}-3\textbf{b})[/tex]
[tex]10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})[/tex]
[tex]-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})[/tex]
[tex]2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})[/tex]
