If it's in $\displaystyle r^3$, can you still do it if there is 4 vectors but each have x y and z?
Do you want to ask whether more than n vectors from $\displaystyle \scriptstyle\mathbb{R}^n$ (here n=3) can be linearly independent? - If so, the answer is no, because a system of n (here 3) homogeneous linear equations in more than n variables (here 4) always has non-trivial solutions.
Or, in fewer words: 4 vectors from $\displaystyle \scriptstyle\mathbb{R}^3$ cannot be linearly independent (they are necessarily linearly dependent).