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

1

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

Let the point A (1, 0, -1) and B (1, -1, 1)

So, the equation of line (x-1)/1= (y-0)/-1 = (z+1)/1

Magnitude is given by = √(1)2 + (-1)2 + (1)2 = √3

Direction cosine to the normal to the plane are 1/√3, -1/√3, 1/√3