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

A variable plane which is at a constant distance 3p 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/(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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A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)=(k)/(p^(2))x^(2)y^(2)z^(2), then root(5)(2k) is

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

If a circle of constant radius 3k passes through the origin and meets the axes at Aa n dB , prove that the locus of the centroid of triangle OA B is a circle of radius 2cdot

Find the equation of the plane, which meets the axes in A,B,C given that centroid of the triangle ABC is the point (alpha, beta, gamma) .

BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE
  1. Find the equation of the plane through the point (-1, -1, 2) and (3, 4...

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

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  3. A variable plane which is at a constant 6 p from the origin meets the ...

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  4. Show that the lines (x-1)/(2)=(y-3)/(4)=-z and (x-4)/(2)=(y-1)/(-2)=(z...

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

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  6. Prove that the lines : (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-...

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

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  8. Find the vector equation of the plane through the intersection of the ...

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  9. Find the equation of the plane through the intersection of the planes ...

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  10. Find the equation of the straight line through the point (1,-3,2) and ...

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  11. Find the equation of the straight line passing through the point (2,3,...

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  12. Find the shortest distance between the line vec(r)=hat(i)-7hat(j)-2hat...

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  13. Find the equation of the plane through the point (1,1,1), parallel to ...

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  14. Find the distance between the point with position vector -hat(i)-5hat(...

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  15. Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z ...

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  16. Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5...

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  17. Find the foot of perpendicular drawn from origin to the plane 2x+3y+4z...

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

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

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  20. Find the shortest distance between the lines whose vector equations ar...

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