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A variable plane is at a constant distan...

A variable plane is at a constant distance `p` from the origin and meets the coordinate axes in `A , B , C` . Show that the locus of the centroid of the tehrahedron `O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot`

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A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tetrahedron O A B C is x^(-2)+y^(-2)+z^(-2)=16p^(-2)

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 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 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 triangle ABC is 1/x^2+1/y^2+1/z^2=1/p^2 .

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A,B anc C, then the locus of the centroid of Delta ABC is :

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that eh locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

A circle of constant radius r passes through the origin O and cuts the axes at A and B. Show that the locus of the foot of the perpendicular from O to AB is (x^2+y^2)^2(x^(-2)+y^(-2))=4r^2 .

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 3k passes through the origin O and meets the coordinate axes at Aa n dB , then the locus of the centroud of triangle O A B 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

RD SHARMA ENGLISH-THE PLANE -All Questions
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  2. Find the equation of a plane passing through the point P(6,\ 5,\ 9) an...

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

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  4. A variable plane at a constant distance p from the origin meets the co...

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  5. Find the distance of the point 2 hat i- hat j-4 hat k from the plane ...

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  6. Find the distance of the point (2, 3, -5) from the plane x+2y-2z-9=0.

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  7. Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the...

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  8. Find the equations of the plane parallel to the plane x-2y+2z-3=0\ an...

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  9. Find the distance of the point (2, 3, 5) from the xy-plane.

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  10. If the product of distances of the point (1,1,1) from the origin and p...

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  11. Find the distance between the point (7,2,4) and the plane determined b...

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  12. Find the distance between the planes 2x-y+2z=4 and 6x-3y+6z=2.

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  13. Prove that the four points having position vectors are non-coplanar: ...

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  14. Find the equation of the plane mid parallel to the planes 2x-2y+z+3=0\...

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  15. Reduce the equation of line x-y+2z=5a d n3x+y+z=6 in symmetrical fo...

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  16. Find dy/dx if x=ay+b

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  17. If the line -> r=\ ( hat i-2 hat j+ hat k)+lambda(2 hat i+ hat j+2 ha...

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  18. Find the equation of the plane passing through the line of intersectio...

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

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

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