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A variable plane is at a distance, k fro...

A variable plane is at a distance, k from the origin and meets the coordinates axis in A, B , C. Then, the locus of the centroid of `triangleABC` is

A

`x^(-2)+y^(-2)+z^(-2)=k^(-2)`

B

`x^(-2)+y^(-2)+z^(-2)=4k^(-2)`

C

`x^(-2)+y^(-2)+z^(-2)=16k^(-2)`

D

`x^(-2)+y^(-2)+z^(-2)=9k^(-2)`

Text Solution

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D
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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Exercise
  1. Find the vector equation of the plane in which the lines vecr=hati+ha...

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  2. The Cartesian equation of the plane vecr=(1+lamda-mu)hati+(2-lamda)hat...

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  3. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

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  4. The vector equation of the line of intersection of the planes vecr.(2h...

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  5. A straight line vecr=veca+lambda vecb meets the plane vecr. vec n=0 at...

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  6. The equation of the plane passing through three non - collinear points...

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  7. The length of the perpendicular from the origin to the plane passing t...

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  8. The equation of the plane containing the line (x-x1)/l=(y-y1)/m=(z-...

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  9. Find the shortest distance between the following pairs of lines whose ...

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  10. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  11. The direction ratios of a normal to the plane passing throuhg (0,0,1)...

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  12. A variable plane is at a distance, k from the origin and meets the coo...

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  13. Find the equation of the plane perpendicular to the line (x-1)/2=(y...

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  14. Find the equation of the plane through the points (2,2,1) and (9,3,6) ...

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  15. The equation of the plane containing the two lines (x-1)/2=(y+1)/(-1...

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  16. The direction ratios of the normal to the plane passing through the po...

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  17. The equation of a plane through the point (2, 3, 1) and (4, -5, 3) a...

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  18. The angle between the lines (x+4)/(1) = (y-3)/(2) = (z+2)/(3) and (x)/...

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  19. The equation of the plane which is perpendicular bisector of the line ...

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  20. If the position vectors of the point A and B are 3hat(i)+hat(j)+2hat(k...

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