If `P(0,1,2),\ Q(4,-2,1)a n d\ O(0,0,0)` are three points then `angle P O Q=` a. `pi/6` b. `pi/4` c. `pi/3` d. `pi/2`

Explanation

To find the angle \( \angle POQ \) formed by the points \( P(0, 1, 2) \), \( Q(4, -2, 1) \), and \( O(0, 0, 0) \), we will use the concept of vectors and the cosine rule in 3D geometry.

### Step 1: Define the vectors
We can define the vectors \( \vec{OP} \) and \( \vec{OQ} \) as follows:
- \( \vec{OP} = P - O = (0 - 0, 1 - 0, 2 - 0) = (0, 1, 2) \)
- \( \vec{OQ} = Q - O = (4 - 0, -2 - 0, 1 - 0) = (4, -2, 1) \)

### Step 2: Calculate the magnitudes of the vectors
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