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 direction cosine of the normal to the plane x - y + z = 4 are: |
$\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ $-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ $\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}$ $-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}$ |
$\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ |
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
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