Find the coordinates of a point on the `(x-1)/2=(y+1)/(-3)=z` atg a distance `4sqrt(14)` from the point `(1,-1,0)dot`

Explanation

To find the coordinates of a point on the line defined by \((x-1)/2 = (y+1)/(-3) = z\) that is at a distance of \(4\sqrt{14}\) from the point \(P(1, -1, 0)\), we can follow these steps:

### Step 1: Parameterize the Line
The line can be expressed in terms of a parameter \(\lambda\). We can set:
\[ \frac{x-1}{2} = \frac{y+1}{-3} = z = \lambda \]
From this, we can express the coordinates \(x\), \(y\), and \(z\) in terms of \(\lambda\):
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