Answer
True.
Work Step by Step
By Theorem 7, we know that a set of vectors is linearly dependent if and only if at least one of the vectors in the set is a linear combination of other vectors in the set. Hence, at least one of the vectors in $\{\vec{v}_{1},\vec{v}_{2},\vec{v}_{3}\}$ must be a linear combination of others in the set, and adding another vector $\vec{v}_{4}$ to the set does not change that fact (e.g., if $\vec{v}_{1}+\vec{v}_{2}=\vec{v}_{3}$, then $\vec{v}_{1}+\vec{v}_{2}+0\vec{v}_{4}=\vec{v}_{3}$).
