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A variable plane makes with the co-ordin...

A variable plane makes with the co-ordinates plane, tetrahedron of contant volume `64 k^3` Then the locus of the centroid of tetrahedron is the surface.

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O(0, 0, 0), A(5, 0, 0), B(5, 5, 0), C(0, 5, 5), D(0, 0, 5), E(5, 0, 5) F(5, 5, 5), G(0, 5, 0)
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KUMAR PRAKASHAN-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Points (-3, 1, 2), (3, -1, 2) and (-3, 1, -2) are in which octants ?

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  2. A, B and C are foot of perpendicular from point P(-5, 3, 7) on XY, YZ,...

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  3. Give the coordinate of point A, B and C if it denotes the perpendicula...

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  4. A variable plane makes with the co-ordinates plane, tetrahedron of con...

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  5. If the distance between the points (x, -8, 4) and (3, -5, 4) is 5 unit...

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  6. Find the equation of the set of the points P such that its distance fr...

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  7. Find point on Y-axis which is of the distance sqrt10 from point (1, 2,...

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  8. Find distance of the point (3, 4, 5) from Y-axis.

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  9. Find coordinates of the point which of the equidistance from O(0, 0, 0...

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  10. Find co-ordinates of the point which divides line segment joining poin...

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  11. Find co-ordinates of the point which divides line segement joining poi...

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  12. In which ratio XY plane divides line segment joining points (2, 4, -3)...

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  13. Show that the points P(-2, 3, 5), Q(1, 2, 3) and R(7, 0, -1) are colli...

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  14. Find the centroid of a triangle, the mid-point of whose sides are D(1,...

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  15. A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are given points. In which r...

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  16. In which ratio the plane x + y + z = 5 divides line segment joining po...

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  17. A(1, 2, 3), B(0, 4, 1) and C(-1, -1, -3) are verticies of DeltaABC. Fi...

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  18. Mid points of sides at DeltaABC are (-2, 3, 5), (4, -1, 7) and (6, 5, ...

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