Find the coordinates of the foot of the perpendicular drawn from the point `A(1,2,1)` to the line joining `B(1,4,6)a n dC(5,4,4)dot`

Explanation

To find the coordinates of the foot of the perpendicular drawn from the point \( A(1, 2, 1) \) to the line joining points \( B(1, 4, 6) \) and \( C(5, 4, 4) \), we will follow these steps:

### Step 1: Find the direction ratios of the line BC
The direction ratios of the line joining points \( B \) and \( C \) can be calculated using the coordinates of the points:
- \( B(1, 4, 6) \)
- \( C(5, 4, 4) \)

The direction ratios \( \vec{BC} \) are given by:
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