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Prove that the point A (0,0,0),B(2,0,0),...

Prove that the point A (0,0,0),B(2,0,0),`C(1,sqrt3,0)` and `D(1,1/sqrt3, (2sqrt2)/sqrt3)` are the vertices of a regular tetrahedron.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the locus of a point which is equidistant from the points (3,2,1...

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  2. Find the point in the XY-plane which is equidistant from the points (2...

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  3. Prove that the point A (0,0,0),B(2,0,0),C(1,sqrt3,0) and D(1,1/sqrt3, ...

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  4. Find the coordinates of the point which divides the join of the points...

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  5. Find the points on the line segment PQ situated at 2/3 of the distan...

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  6. Find the points on the line segment PQ situated at 2/3 of the distan...

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  7. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

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  8. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

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  9. Find the coordinates of the point which is three fifth of the way (3,4...

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  10. Find the ratio in which the line segment joining : (1,2,3) and (-3,4,-...

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  11. If A and B are the points (-3,4,-8) and (5,-6,4) respectively, find th...

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  12. Using section formula, prove that the three points (-2,3,5),(1,2,3) an...

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

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

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

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

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

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

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

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