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