Answer
On the same line.
Work Step by Step
If $\mathbf{P_1}, \mathbf{P_2}, \mathbf{P_3}$ are points over the same line, vectors $\overrightarrow{\mathbf{P_1P_2}}=\mathbf{u}$ and $\overrightarrow{\mathbf{P_1P_3}}=\mathbf{v}$ are parallel.
We have that
$$\overrightarrow{\mathbf{P_1P_2}}=\langle 3,-4,-3\rangle-\langle 1,0,1\rangle=\langle 3-1,-4-0,-3-1\rangle=\langle 2,-4,-4\rangle$$
$$\overrightarrow{\mathbf{P_1P_3}}=\langle 4,-6,5\rangle-\langle 1,0,1\rangle=\langle 3,-6,-6\rangle$$
We note that $\overrightarrow{\mathbf{P_1P_2}}=2\langle 1,-2,-2\rangle=\frac{2}{3}\langle 3,-6,-6\rangle=\frac{2}{3}\mathbf{u}$ and $\mathbf{v}=\frac{3}{2}\mathbf{u}$, $\overrightarrow{\mathbf{u}}$ and $\overrightarrow{\mathbf{v}}$ parallel and are over the same line.
