How to show that the vector value function describes the motion of a particle

Question

The vector value function is $r(t)= (2i+2j+k)+cos(t)((1/\sqrt{2})i-(1/\sqrt{2})j)+sin(t)((1/\sqrt{3})i+(1/\sqrt{3})j+(1/\sqrt{3})k)$ And the particle is moving in the circle of radius 1 centered at the point $(2,2,1)$ and lying in the plane $x+y-2z=2$