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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 opposite faces are concurrent.

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i. Show that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent. ii. Show that the joins of the midpoints of the opposite edges of a tetrahedron intersect and bisect each other.

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Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

Two coplanar triangles ABC and PQR re such that the lines drawn through the vertices of /_\ABC parallel to the sides of /_\PQR are concurrent. Prove that the lines drawn through the vertices of /_\PQR parallel to sides of /_\ABC are concurrent.

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Prove that the medians of a triangle are concurrent.

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Show that the line joining one vertex of a parallelogram to the mid-point of an opposite side trisects the diagonal and is trisected thereat.

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RD SHARMA ENGLISH-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-All Questions
  1. Find the point on y-axis which is equidistant from the points (3,1,2) ...

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  2. Prove that the triangle formed by joining the three points whose co...

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  3. Prove that the lines joining the vertices of a tetrahedron to the ce...

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  4. Using the section formula, prove that the three points A(-2,3,5),B(1...

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  5. Find the coordinates of the points which trisect the line segment A ...

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  6. Find the ratio in which the join the A(2,1,5)a n dB(3,4,3) is divided ...

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  7. Planes are drawn parallel to the coordinate planes through the point P...

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  8. Name the octants in which the following points lie: (5,2,3)

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  9. Name the octants in which the following points lie: (-5,-4,7)

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  10. Name the octants in which the following points lie: (-5,4,3)

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  11. Name the octants in which the following points lie: (-5,-3,-2)

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  12. Name the octants in which the following points lie: (4,-3,5)

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  13. Name the octants in which the following points lie: (2,-5,-7)

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  14. Name the octants in which the following points lie: (7,4,-3)

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  15. Name the octants in which the following points lie: (-7,2,-5)

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  16. Find the image of: (-2,3,4) in the yz-planes.

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  17. Find the image of: 5,2,-7) in the xy-planes.

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  18. Find the image of: (-4,0,0) in the xy-planes.

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  19. Find the image of: (-5,4,-3) in the xz-planes.

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  20. Find the image of point: (-5,0,3) in the xz-planes.

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