Suppose the floor of a hotel is made up of mirror polished Salvatore stone. There is a large crystal chandelier attached to the ceiling of the hotel room. Consider the floor of the hotel room as a plane having the equation x – y + z = 4 and the crystal chandelier is suspended at the point (1, 0, 1).

Based on the above answer the following:

**1.** Find the direction ratios of the perpendicular from the point (1, 0, 1) to the plane x – y + z = 4.

a. (-1, -1, 1)

b. (1, -1, -1)

c. (-1, -1, -1)

d. (1, -1, 1)

**2.** Find the length of the perpendicular from the point (1, 0, 1) to the plane x – y + z = 4.

a. \(\cfrac2{\sqrt3}\) units

b. \(\cfrac4{\sqrt3}\) units

c. \(\cfrac6{\sqrt3}\) units

d. \(\cfrac8{\sqrt3}\)units

**3.** The equation of the perpendicular from the point (1, 0, 1) to the plane x – y + z = 4 is

**4. **The equation of the plane parallel to the plane x – y + z = 4, which is at a unit distance from the point (1, 0, 1) is

a. x – y + z + (2 - √3 )

b. x – y + z - (2 + √3 )

c. x – y + z + (2 + √3 )

d. Both (a) and (c)

**5.** The direction cosine of the normal to the plane x – y + z = 4 is