How can I show that $\vec{v}$ can be any vector in a plane where $\vec{v} = a_1\vec{v}_1+a_2\vec{v}_2$?
All vectors start at the origin, $a_1$ and $a_2$ are scalars, $\vec{v}_1$ and $\vec{v}_2$ are vectors that are not scalar multiples of each other.
I know two vectors that are not scalar multiples of each other are on a plane, but I don't know how to show this. (I think "linearly independent" is the right term?)
(This is from Linear and Geometric Algebra by A. Macdonald — I am self studying between semesters.)