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Show that the sum of the reciprocals of the intercepts on rectangular axes made by a fixed plane is same for all systems of rectangular axes, with a given origin.

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. A variable plane passes through a fixed point a,b,c and meet the co-or...

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  2. A variable plane moves so that the sum of reciprocals of its intercept...

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  3. Show that the sum of the reciprocals of the intercepts on rectangular ...

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  4. Find the equations of the bisector planes of the angle between the pla...

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  5. In the following case, determine whether the given planes are parallel...

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  6. In the following case, determine whether the given planes are parallel...

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  7. In the following case, determine whether the given planes are parallel...

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  8. ਪIn the following case, determine whether the given planes are paralle...

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  9. In the following case, determine whether the given planes are parallel...

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  10. What is the point of intersection of the line x=y=z with the plane x+2...

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  11. Find the angle between the lines in which the planes: 3x-7y-5z=1, 5x-1...

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  12. Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) li...

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  13. Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in t...

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  14. Find the vector equation of the line passing through the point (3,1,2)...

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  15. Find the point where the line (x+1)/2=(y+2)/3=(z+3)/4 meets the plane ...

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  16. Find the angle between the line : (2hati+3hatj+4hatk)+lambda(2hati+3ha...

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  17. Find the angle between the line joing (3,-4,-2) and(12, 2, 0) and the ...

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  18. Find the angle between the line : (x+1)/2=y/3=(z-3)/6 and the plane 10...

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  19. Find the angle between the line (x+1)/2 = y/3 = (z-3)/6 and the plane ...

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  20. Find the distance of the point (-1, -5, -10) from the point of interse...

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