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Prove that if a plane has intercepts a,b...

Prove that if a plane has intercepts a,b,c and is at a distance of p units from the origin, then `1/a^2+1/b^2+1/c^2=1/p^2`.

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Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then 1/a^2 + 1/b^2 + 1/c^2 = 1/p^2

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The differential equation of all straight lines which are at a constant distance p from the origin, is (a) (y+xy_1)^(2)=p^(2) (1+y_(1)^2) (b) (y-xy_(1)^(2))=p^(2) (1+y_(1))^(2) ( c ) (y-xy_(1))^(2)=p^(2) (1+y_(1)^(2)) (d) None of these

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/p^2=1/a^2+1/b^2 .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that (1)/(p^(2)) = (1)/(a^(2)) +(1)/(b^(2)) .

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A variable plane which is at a constant distance 6 p from the origin meets the axes in points A, B and C respectively. Show that the locus of the centroid of Delta ABC is 1/x^2+1/y^2+1/z^2=1/(4p^2)

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. The equation of the plane passing through the line of intersection of ...

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  2. The point P is the intersection of the straight line joining the point...

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  3. If the lines (x-2)/1=(y-3)/1=(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 ar...

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  4. Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is

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  5. The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z...

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  6. The angle between the lines whose direction cosines satisfy the equa...

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  7. The distance of the point (1,0,2) from the poitn of intersection of th...

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  8. The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...

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  9. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  10. The distance of the point (1, -5, 9) from the plane x-y+z=5 measured a...

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  11. If a line has direction ratios <2,-1,-2>, then what are its direction ...

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  12. Find the Cartesian equation of the following plane: vecr cdot (hati+ha...

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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 area of the triangle whose vertices are : A(1,2,3), B(2,-1,4)...

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  15. Find the equations of the straight line passing through the point (2,...

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  16. Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.

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  17. Find the equation of the plane passing through the point(-1, 3, 2) and...

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  18. Prove that if a plane has intercepts a,b,c and is at a distance of p u...

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  19. A line makes angles alpha, beta, gamma, delta with the diagonals of a ...

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  20. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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