The floor of the banquet hall in a hotel is made of polished stone. There is a large chandelier attached to the ceiling of the hall. Consider floor of the hotel as a plane having the equation x - y + z = 4 and chandelier is suspended at the point (1, 0, 1) from the wall.

On the basis of above information, answer the following questions.

The equation of the perpendicular from the point (1, 0, 1) to the plane x - y + z = 4 is: 

$\frac{x-1}{1}=\frac{y}{-1}=\frac{1-z}{-1}$

The correct answer is Option 2: $\frac{x-1}{1}=\frac{y}{-1}=\frac{1-z}{-1}$

The equation of the plane is: x − y + z = 4

For a plane of the form ax + by + cz + d = 0, the normal vector to the plane is (a, b, c).
Therefore, the normal vector to the plane is (1, −1, 1).

A line perpendicular to the plane must have the same direction ratios as the normal vector.
Hence the direction ratios of the required line are (1, −1, 1).

The symmetric equation of a line passing through a point (x₁, y₁, z₁) with direction ratios (a, b, c) is

(x − x₁)/a = (y − y₁)/b = (z − z₁)/c

Substituting: (x₁, y₁, z₁) = (1, 0, 1) and (a, b, c) = (1, −1, 1):

(x − 1)/1 = (y − 0)/(−1) = (z − 1)/1

This can also be written as: (x − 1)/1 = y/(−1) = (1 − z)/(−1)

which matches Option (2).