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Prove that the lines joining the vertice...

Prove that the lines joining the vertices of a tetrahedron to the centroids of the opposite faces are concurrent.

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MODERN PUBLICATION-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Prove that the lines joining the vertices of a tetrahedron to the cent...

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  2. A point is on x-axis. What are its y-co-ordinate and z-co-ordinate ?

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  3. A point is in the XZ-plane. What can you say about its y-co-ordinate ?

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  4. In the figure, find the reflection of P(x, y, z) in the: XY-plane.

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  5. In the figure, find the reflection of P(x, y, z) in the: YZ-plane.

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  6. In the figure, find the reflection of P(x, y, z) in the: ZX-plane.

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  7. Find the octant in which the following points lie : (- 3, 1, 2).

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  8. Find the octant in which the following points lie : (3, 1, - 2) .

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  9. Find the octant in which the following points lie : (- 3, 1, - 2) .

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  10. Find the octant in which the following points lie : (- 3, - 1, - 2).

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  11. Write the perpendicular distance of the point (x, y, z) from the three...

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  12. The co-ordinates of a point are (1, -2, 7). Find the co-ordinates of t...

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  13. Write the co-ordinates of the feet of perpendicular from the point (a,...

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  14. Find the image of the point in the specified plane : (5,4,-3) in th...

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  15. Find the image of the point in the specified plane : (-2,0,0) in the...

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  16. Find the image of the point in the specified plane : (-3, 4, 7) in t...

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  17. Find the image of the point in the specified plane : (- 7, 2, -1) in...

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  18. Find the image of the point in the specified plane : (- 4,0, 1) in t...

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  19. Find the perpendicular distances of the point P (a, b, c) from the co-...

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  20. Planes are drawn parallel to co-ordinate planes through the points (3,...

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  21. Fill in the blanks : The x-axis and y-axis, taken together, determin...

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