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

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CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. A tetrahedron has vertices of O(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C...

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  2. The radius of the circle in which the sphere x^(2)=y^(2)+z^(2)+2z-2y-4...

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  3. A sphere of constant radius 2k passes through the origin and meets t...

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  4. A plane passes through a fixed point (a,b,c). The locus of the foot of...

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  5. Equation of the plane containing the straight line (x)/(2)= (y)/(3)= (...

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

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  7. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

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  8. The vector equation of the plane passing through the origin and the ...

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  9. The lines vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( v...

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  10. The projection of the line (x+1)/(-1)=(y)/(2)=(z-1)/(3) on the plane x...

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  11. The direction cosines of a line satisfy the relations lamda(l+m)=nandm...

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  12. The intercepts made on the axes by the plane which bisects the line jo...

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  13. The pair of lines whose direction cosines are given by the equation...

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  14. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha,...

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  15. A line with positive direction cosines passes through the point P(2, –...

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  16. The value of k such that (x-4)/1=(y-2)/1=(z-k)/2 lies in the plane 2x-...

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  17. The equation of the plane passing through lines (x-4)/1=(y-3)/1=(z-...

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  18. The line through hat i+3 hat j+2 hat k and | to the line vec r=( hat...

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  19. The equation of the plane through the line of intersection of the plan...

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  20. The three planes 4y+6z=5,2x+3y+5z=5 and 6x+5y+9z=10 (a) meet in a poi...

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