Find the coordinates of the point where the line `("x"+1"")/2=("y"+2)/3=("z"+3)/4` meets the plane `"x"+"y"+4"z"=6.`

Explanation

To find the coordinates of the point where the line \(\frac{x+1}{2} = \frac{y+2}{3} = \frac{z+3}{4}\) meets the plane \(x + y + 4z = 6\), we can follow these steps:

### Step 1: Parameterize the Line
We start by letting the common ratio equal a parameter \(t\):
\[ \frac{x+1}{2} = \frac{y+2}{3} = \frac{z+3}{4} = t \]

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