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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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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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A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. show that the locus of the centroid of the triangle ABC is x^-2+y^-2+z^-2=p^-2 .

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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)) .

PSEB-THREE DIMENSIONAL GEOMETRY-Exercise
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  4. If the lines (x-1)/-3 = (y-2)/2k = (z-3)/2 and (x-1)/3k = (y-1)/1 = (z...

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  5. Find the vector equation of the line passing through (1, 2, 3) and per...

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  6. Find the equation of the plane passing through (a, b, c) and parallel ...

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  13. If O be the origin and the coordinates of P be (1, 2, – 3), then find ...

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  14. Find the equation of the plane which contains the line of intersection...

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  15. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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  16. Find the vector equation of the line passing through (1, 2, 3) and par...

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

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