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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. Find the ratio in which 2x+3y+5z=1 divides the line joining the points...

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  2. Given that A (3, 2,-4), B(5, 4, -6) and C(9, 8, -10) are collinear. Fi...

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  3. Using Section formula, show that the points A (2,- 3, 4), B (-1, 2, 1)...

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  4. Given that p(3,2,-4) , Q (5,4, -6) and R (9,8,-10) are collinear find...

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  5. If the mid points of the sides of a triangle are (1, 5, -1), (0, 4, -2...

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  6. Show that the points (-1,2,1), (1,-2,5), (4,-7,8) and (2,-3,4) are ver...

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  7. Three vertices of parallelogram ABCD are A(3,-1,2), B(1,2,-4), C(-1,1,...

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  8. Show that the points A(1, 2, 3,), B (-1, -2. -1), C(2, 3, 2) and D(4, ...

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  9. The vertices of triangle are A(1,1,2),B(4,3,1) and C(2,3,5). A vector ...

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  10. Find the lengths of the medians of the triangle A (0, 0, 6), B (0, 4, ...

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  11. The centroid of a triangle ABC is at the point (1,1,1). If the coordin...

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  12. If the origin is the centroid of the triangle PQR with vertices P(2a,2...

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  13. Planes are drawn through the points (5, 0, 2) and (3, - 2, 5) parallel...

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  14. Prove that the lines joining the vertices of a tetrahedron to the cent...

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  15. Find the lengths of the edges of the rectangular parallelopiped formed...

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  16. Verify that (0, 7, 10) , (-1,6,6) and (-4, 9,6) are the vertices of a ...

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  17. Show that the points : (4, 7, 8), (2, 3, 4), (- 1, - 2, 1), (1, 2, 5) ...

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  18. Show that the points (5, - 1, 1),(7, - 4, 7), (1, - 6, 10) and (- 1, -...

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  19. If A and B be the points (3,4,5) and (-1,3,-7) respectively, find the ...

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  20. Find the co-ordinates of the point, which is equidistant from four poi...

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