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A variable plane is at a constant distan...

A variable plane is at a constant distance 3r from the origin and meets the axes in A, B and C. Show that the locus of the centroid of the `Delta ABC` is `x^(-2) + y^(-2) + z^(-2) = r^(-2)`.

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The correct Answer is:
`r^(-2)`
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ARIHANT PRAKASHAN-THREE DIMENSIONAL GEOMETRY -TOPIC -2- PRACTICE QUESTIONS
  1. Find the equation of the plane with intercept 2, 3 and 4 on the X, Y a...

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  2. Show that the normals to the planes oversettor.(overset^i-overset^j+ov...

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  3. Find the vector equation of a plane which is at a distance of 3 units ...

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  4. If the position vectors of two points A ans B are 3overset^i+2overset^...

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  5. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

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  6. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  7. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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  8. Prove that the four points (0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1...

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  9. Find the equation of the plane passing through the line x = y = z and ...

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  10. Find the image of the point (-2,0,3) with respect to the plane y = 3.

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  11. Find the equation of a plane biscting the line segment joining (-1,4,3...

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  12. Find the equation of the plane passing through the points (-2, 3, 5), ...

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  13. Find the equation of the plane passing through the intersection of the...

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  14. Write the equation of the plane 3x-4y+6z-12=0 in intercept from and he...

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  15. Find the distance between the following parallel planes. 2x - y + 2z...

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  16. Write the equation of the plane 2x-3y+5z+1=0 in normal from and find i...

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  17. A variable plane is at a constant distance 3r from the origin and meet...

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  18. Find the image of the point (2, 3, 4) with respect to the plane x - y ...

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  19. Find the equation of the plane Passing through the intersection of the...

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  20. A variable plane is at a constant distance p from the origin and meets...

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