Kinematics Questions

The position vector of a particle $\vec{R}$ as a function of time is given by:
$$\vec{R}=4\sin (2\pi t)\hat{i}+4\cos (2\pi t)\hat{j}$$
Where $R$ is in meters, $t$ is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along $x$ - and $y$ -directions, respectively. Which one of the following statements is wrong for the motion of particle?

Two particles $A$ and $B$ move with constant velocities ${\vec{v}}_1$ and ${\vec{v}}_2$. At the initial moment their position vectors are ${\vec{r}}_1$ and ${\vec{r}}_2$ respectively. The condition for particles $A$ and $B$ for their collision is: