If a line drawn from the point `A(1, 2,1)` is perpendicular to the line joining `P(1, 4, 6) and Q(5, 4, 4)`, then find the coordinates of the foot of the perpendicular.

Explanation

To solve the problem of finding the coordinates of the foot of the perpendicular from point A(1, 2, 1) to the line joining points P(1, 4, 6) and Q(5, 4, 4), we can follow these steps:

### Step 1: Determine the direction vector of line PQ
The direction vector \( \vec{PQ} \) can be calculated as:
\[ \vec{PQ} = \vec{Q} - \vec{P} = (5 - 1, 4 - 4, 4 - 6) = (4, 0, -2) \]

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