Find the co-ordinates of the foot of perpendicular and its perpendicular distance drawn from the point `(1,3,4)` to the plane `2x-y-2z+3=0.`Also find the image of the point `(1,3,4)` in the plane.

Explanation

To solve the problem of finding the coordinates of the foot of the perpendicular from the point \( P(1, 3, 4) \) to the plane given by the equation \( 2x - y - 2z + 3 = 0 \), and also to find the image of the point in the plane, we will follow these steps:

### Step 1: Identify the normal vector of the plane
The equation of the plane is given as \( 2x - y - 2z + 3 = 0 \). We can identify the normal vector \( \vec{n} \) of the plane from the coefficients of \( x, y, z \):
\[ \vec{n} = (2, -1, -2) \]

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