Find the length of the perpendicular drawn from point `(2,3,4)` to line `(4-x)/2=y/6=(1-z)/3dot`

Explanation

To find the length of the perpendicular drawn from the point \( P(2, 3, 4) \) to the line given by the symmetric equations \( \frac{4-x}{2} = \frac{y}{6} = \frac{1-z}{3} \), we can follow these steps:

### Step 1: Convert the line equations into parametric form
The symmetric equations can be expressed in parametric form. Let \( \lambda \) be the parameter:
- From \( \frac{4-x}{2} = \lambda \), we have \( x = 4 - 2\lambda \).
- From \( \frac{y}{6} = \lambda \), we have \( y = 6\lambda \).
- From \( \frac{1-z}{3} = \lambda \), we have \( z = 1 - 3\lambda \).

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