A rigid body is spinning about a fixed point (3,-2,-1) with an angular velocity of 4 rad/s, the axis of rotation being in the direction of (1,2,-2). Find the velocity of the particle at point (4,1,1).

Explanation

To find the velocity of the particle at point \( P(4, 1, 1) \) given that a rigid body is spinning about a fixed point \( A(3, -2, -1) \) with an angular velocity of \( \omega = 4 \, \text{rad/s} \) in the direction of the vector \( (1, 2, -2) \), we can follow these steps:

### Step 1: Define the angular velocity vector
The angular velocity vector \( \vec{\omega} \) can be expressed as:
\[ \vec{\omega} = \omega \hat{n} \]
where \( \hat{n} \) is the unit vector in the direction of the axis of rotation.
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