A particle moves so that its position vector is given by r→ = cos ωt x→ +sin ωt y^, where ω is a constant which of the following is true?

r→ = cosωt x^+ sinωt y^v→ = −ωsinωt x^+ ωcosωt y^a→ = −ω2cosωt x^+ ωsinωt y^ = −ω2r→r→.v→ = 0  hence  r→ ⊥ v→ a→ is directed towards the origin.