A particle moves so that its position vector is given by

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A particle moves so that its position vector is given by r^{^→} = cos ωtx̂ + sin ωtŷ . Where ω is a constant. Which of the following is true?

1. Velocity and acceleration both are perpendicular to r^{^→}
2. Velocity and acceleration both are parallel to r^{^→}
3. Velocity is perpendicular to r^{^→} and acceleration is directed towards the origin
4. Velocity is perpendicular to r^{^→} and acceleration is directed away from the origin

Correct Option: C

Given : Position vector r^{^→} = cos ωt x̂ + sin ωt ŷ
∴ Velocity , v^{^→} = – ωsin ωt x̂ + ωcos ωt ŷ
and acceleration , a^{^→} = –ω² cos ωt x̂ – ω²sin ωt ŷ = – ω² r^{^→}
r^{^→} . v^{^→} = 0 hence r^{^→} ⊥ v^{^→} and
a^{^→} is directed towards the origin.