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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

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1 Answer

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1. (d) (1, -1, 1)

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

3. (c) \(\cfrac{x-1}1=\cfrac{y}{-1}=\cfrac{z-1}1\)

4. (d) Both (a) and (c)

5. (b) \(\Big(\cfrac{1}{\sqrt3},\cfrac{-1}{\sqrt3},\cfrac{1}{\sqrt3}\Big)\)

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