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A sphere of constant radius `k ,` passes through the origin and meets the axes at `A ,Ba n d Cdot` Prove that the centroid of triangle `A B C` lies on the sphere `9(x^2+y^2+z^2)=4k^2dot`

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`4 K^(2)`
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A sphere of constant radius k ,passes through the origin and meets the axes at A,B and C. Prove that the centroid of triangle ABC lies on the sphere 9(x^(2)+y^(2)+z^(2))=4k^(2)

If a sphere of constant radius k passes through the origin and meets the axis in A,B,C then the centroid of the triangle ABC lies on :

A circle of constant radius 2r passes through the origin and meets the axes in 'P' and 'Q' Locus of the centroid of the trianglePOQ is :

If a circle of constant radius 3c passes through the origin and meets the axes at AandB prove that the locus of the centroid of /_ABC is a circle of radius 2c

A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C What is the locus of the centroid of the triangle ABC?

A sphere of constant radius 2k passes through the origin and meets the axes in A,B, and C . The locus of a centroid of the tetrahedron OABC is a.x^(2)+y^(2)+z^(2)=4k^(2)bx^(2)+y^(2)+z^(2)=k^(2) c.2(k^(2)+y^(2)+z)^(2)=k^(2)d none of these

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at AandB,then the locus of the centroud of triangle OAB is (a)x^(2)+y^(2)=(2k)^(2)(b)x^(2)+y^(2)=(3k)^(2)(c)x^(2)+y^(2)=(4k)^(2)(d)x^(2)+y^(2)=(6k)^(2)

circle of radius 3k passes through (0,0) and cuts the axes in A and B then the locus of centroid of triangle OAB is

ML KHANNA-CO-ORDINATE GEOMETRY OF THREE DIMENSION-MISCELLANEOUS EXERCISE(TRUE AND FALSE)
  1. Show that the straight lines whose direction cosines are given by t...

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  2. The equation of the plane through the points (1,1,1),(1,-1,1) and (-7,...

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

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  4. The equation of the plane through the intersection of the planes x-2y+...

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  5. A variable plane at a constant distance p from the origin meets the ax...

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

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  7. A plane a constant distance p from the origin meets the coordinate axe...

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  8. The equation 2x^(2) -6y^(2) - 12z^(2)+18 yz +2zx + xy =0 represents a ...

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  9. The lines (x-1)/1=(y-2)/2=(z-3)/3 and x/2=(y+2)/2=(z-3)/-2 are paral...

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  10. The lines (x-1)/2=(y-2)/2=(z-3)/0 and (x-2)/0=(y+3)/0=(z-4)/1 are pa...

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  11. The plane x-2y+z-6=0 and the line x/1=y/2=z/3 are related as the line ...

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  12. Find the length of the perpendicular from point (3,4,5) on the line (x...

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  13. Find the angle between the lines in which the planes : 3x - 7y - 5z ...

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  14. The lines 2x+3y-4z=0 ,3x-4y+z=7 5x-y-3z+12=0, x-7y+5z-6=0 are parell...

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  15. The lines (x-5)/4=(y-7)/4=(z+3)/-5 and (x-8)/7=(y-4)/1=(z-5)/3 are cop...

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  16. A sphere of constant radius k , passes through the origin and me...

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  17. A variable plane passes through a fixed point (a ,b ,c) and cuts th...

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  18. If any tangent plane to the sphere x^(2) + y^(2) +z^(2) makes interc...

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  19. Two spheres of radii r(1) and r(2), cut orthogonally. The radius of th...

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  20. The smallest radius of the sphere passing through the points (1,0,0), ...

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