Velocity perpendicular to position vector

Particle 1 has position vector $\tvec{r}_1(t) = \cos(t)\tvec{i} + \sin(t)\tvec{j} + \sqrt{\sin(2t)}\,\tvec{k}$ and Particle 2 has position vector $\tvec{r}_2(t) = \sin(t)\tvec{i} + \cos(t)\tvec{j} + \sqrt{\sin(2t)}\,\tvec{k}$, where $t$ is measured in seconds and $t \in \left(0, \frac{\pi}{2}\right)$.

The number of times the velocity of Particle 1 is perpendicular to the position vector $\tvec{r}_2(t)$ during the first $\frac{\pi}{2}$ seconds is