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Two systems of rectangular axes have the...

Two systems of rectangular axes have the same origin. If a plane cuts them at distance `a,b,c and a',b',c'` respectively form the origin, prove that `1/a^2+1/b^2+1/c^2=1/(a'^2)+1/(b'^2)+1/(c'^2)`.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the distance between the parallel planes 2x-y+3z+4=0 and 6x-3y+9z...

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  2. Show that the equation of the plane through the line x/l=y/m=z/n and p...

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  3. Two systems of rectangular axes have the same origin. If a plane cuts ...

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  4. Show that the points P(hati-hatj+3hatk) and Q(3hati+3hatj+3hatk) are e...

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  5. Find in parametric form, the equations of the line x+y+z+1=0, 4x+y-2z+...

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  6. Find the equation of the plane through the line of intersection of the...

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  7. Find the equation of the plane containing the line of intersection of ...

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  8. Find the vector quation of the plane containing the line of intersecti...

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  9. Find the equation of the plane which is perpendicular to the plane 5 x...

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  10. Find the equation of the plane bisectiing the angles between the plane...

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  11. Show that the lines (x+4)/3=(y+6)/5=(z-1)/-2 and 3x-2y+z+5=0=2x+3y+4z-...

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  12. Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z...

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  13. Find the equations of the line through the point (1,2,4) and parallel ...

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  14. Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+...

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  15. Prove that the lines x=py+q, z=ry+s and x=p'y+q'z=r'y+s' are at right ...

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  16. Find the equations of the plane through the intersection of the planes...

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  17. Find the equations of the plane which contains the line of intersectio...

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  18. If a line makes angles of 90^@,60^@ and theta with the x, y and z axis...

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  19. Name the locus of the equation x^2+y^2=0.

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  20. What is the locus of the equations x^2+y^2+z^2=0?

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