A particle moves such that its position vector \(\vec{\text{r}}\)(t) = cos ωt î + sin ωt ĵ where ω is a constant and t is time. Then which of the following statements is true for the velocity \(\vec{\text{v}}\)(t) and acceleration \(\vec{\text{a}}\)(t) of the particle :
1
\(\vec{\text{v}}\) and \(\vec{\text{a}}\) both are parallel to \(\vec{\text{r}}\)
2
\(\vec{\text{v}}\) and \(\vec{a}\) both are perpendicular to \(\vec{\text{r}}\)
3
\(\vec{\text{v}}\) is perpendicular to \(\vec{\text{r}}\) and \(\vec{\text{a}}\) is directed towards the origin
4
\(\vec{\text{v}}\) is perpendicular to \(\vec{\text{r}}\) and \(\vec{\text{a}}\) is directed away from the origin