A particle moves so that its position vector is given by 𝑟⃗=cosωt^x+sinωt^y. Where ω is a constant. Which of the following is true?

Step 1: Velocity and acceleration calculation
𝑟⃗=cosωt^x+sinωt^y (1)
Velocity is given by
𝑣⃗=d𝑟⃗/dt
𝑣⃗=−ωsinωt^x+ωcosωt^y m/s (2)
Acceleration is given by
a⃗=d𝑣⃗/dt
a⃗=−ω²cosωt^x−ω²sinωt^y m/s² (3)
Step 2: Analysing 𝑟⃗,𝑣⃗ and 𝑎⃗
If the dot product between two vectors is zero that means the vectors are perpendicular to each other.
𝑣⃗⋅𝑟⃗=−ωsinωtcosωt+ωsinωtcosωt=0
∴ 𝑣⃗ is perpendicular to 𝑟⃗
a⃗⋅𝑟⃗=−ω²cos²ωt−ω²sin²ωt≠0
∴ 𝑎⃗ is not perpendicular to 𝑟⃗
Negative sign in eqn(3) indicates acceleration is towards the origin (Opposite to 𝑟⃗)
Hence , 𝑣⃗ is perpendicular to 𝑟⃗ and the acceleration is directed towards the origin
∴Option D is the correct answer.