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Using vectors, show that the medians of a triangle are concurrent.

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Prove analytically that the : medians of a triangle are concurrent.

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How many medians can a triangle have ?

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Prove that the perpendicular bisectors of the sides of triangle are concurrent.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Using section formula, prove that the three points (-2,3,5),(1,2,3) an...

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

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  3. Using vectors, show that the medians of a triangle are concurrent.

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  4. Prove that the points A(5,0,2), B(2,-6,0),C(4,-9,6) and D(7,-3,8), tak...

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  5. If three consecutive vertices of a parallelogram are (3,4,-1),(7,10,-3...

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  6. The ends of a side of a parallelogram are (2,5,-3),(3,7,-5) and its di...

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  7. The mid-points of the sides of a triangle are (5,7,11),(0,8,5) and (2,...

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  8. Two vertices of a traingle are (2,-6,4) and (4,-2,3) and its centroid ...

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  9. Find the coordinates of the centroid of a triangle the mid points of w...

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  10. A (3, 2, 0), B(5, 3, 2), C(- 9, 6, -3) are three points forming a tria...

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  11. Calculate the cosine of the angle A of the triangle with vertices A(1,...

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  12. The direction ratios of a vector are <1,-3,-2>, find its direction cos...

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  13. Find the direction cosines of the vectors: 2hati+2hatj-hatk

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  14. Find the direction cosines of the vectors: 6hati-2hatj-3hatk

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  15. Find the direction cosines of the vectors: 3hati+4hatk

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  16. Find the direction cosines of the vectors: hatk

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  17. Find the angles at which the following vectors are inclined to each of...

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  18. Find the angles at which the following vectors are inclined to each of...

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  19. Find the angles at which the following vectors are inclined to each of...

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  20. Find the angles at which the following vectors are inclined to each of...

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