Find the foot of the perpendicular from the point (2,3,-8) to the line `(4-x)/2 =y/6=(1-z)/3`. Find the perpendicular distance from the given point to the line.

Explanation

To find the foot of the perpendicular from the point \( P(2, 3, -8) \) to the line given by the equation \( \frac{4-x}{2} = \frac{y}{6} = \frac{1-z}{3} \), we will follow these steps:

### Step 1: Rewrite the line equation in parametric form
The line equation can be rewritten in parametric form. Let \( k \) be the parameter such that:

\[ \frac{4-x}{2} = k \implies x = 4 - 2k \]
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