Practicing Success
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 plane in the banquet hall parallel to the x - y + z = 4, and at a unit distance from the point (1, 0, 1), is : |
$x-y-z=6+\sqrt{3}$ $x-y+z=2-\sqrt{3}$ $x-2y+z=4$ $x-y+z=4-\sqrt{3}$ |
$x-y-z=6+\sqrt{3}$ |
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 |