The linear momentum of a particle is given by `vec(P)=(a sin t hati- acos t hatj) kg- m//s`. A force `vec(F)` is acting on the particle. Select correct alternative/s:

Options

A. Linear momentum `vec(P)` of particle is always parallel to `vec(F)`
B. Linear momentum `vec(P)` of particle is always perpendicular to `vec(F)`
C. Linear momentum `vec(P)` is always constant
D. Magnitude of linear momentum is constant with respect to time.

Explanation

To solve the problem, we need to analyze the linear momentum of the particle and the force acting on it. The linear momentum is given by:

\[ \vec{P} = A \sin t \hat{i} - A \cos t \hat{j} \]

### Step 1: Differentiate the momentum vector to find the force
The force acting on the particle is given by the time derivative of the momentum:
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