Given vectors $(1, 3, 5), (-2 , -6, -10)$ and $(2, 6 , 10)$ determine whether the linear span of the above is a plane in $\mathbb R^3$.
The vectors are linearly dependent nd hence do not form a basis and it is known that the set of linearly dependent vectors in $R^2$ are collinear.
So based on the above can it be said that linearly dependent vectors in $R^3$ will form a plane.
Your intuition is correct. It can be more rigorously stated, considering that the equation of a plane in $\mathbb R^3$ is :
$$Ax + By + Cz = 0$$
But since your given vectors are linearly dependent, you will arrive at such an equation, thus satisfying the known algebraic expression (form) of a plane.