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Prove that the tetrahedron with vertices...

Prove that the tetrahedron with vertices at the points `O(0,0,0),\ A(0,1,1), B(1,0,1)a n d\ C(1,1,0)` is a regular one.

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RD SHARMA ENGLISH-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-All Questions
  1. Prove that the point A(1,3,0),\ B(-5,5,2),\ C(-9,-1,2)\ a n d\ D(-3,-3...

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  2. Show that the points A(1,3,4),\ B(-1,6, 10),\ C(-7,4,7)a n d\ D(-5,1,1...

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  3. Prove that the tetrahedron with vertices at the points O(0,0,0),\ A(0,...

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  4. Show that the points (3,2,2), (-1,4,2), (0,5,6), (2,1,2) lie on a s...

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  5. Find the coordinates of the point which is equidistant from the four ...

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  6. Find the locus of P\ if\ P A^2+P B^2=2k^2w h e r e\ A\ a n d\ B are po...

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  7. Are the points A(3,6,9),\ B(10 , 20 , 30)a n d\ C(25 ,-41 ,5), the ver...

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  8. Verify the following: (0,7,-10), (1,6,-6) and (4,9,-6) are vertices of...

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  9. Find out whether the points (0, 7, 10), (-1,6,6) and (-4,9,6) are the ...

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  10. Verify the following: (-1,2,1), (1,-2,5), (4,-7,8) and (2,-3,4) are ...

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  11. Verify the following: (5,-1,1),(7,-4,7), (1,-6,10) and (-1,-3,4) are ...

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  12. Find the locus of the points which are equidistant from the points ...

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  13. Find the locus of the point, the sum of whose distances from the point...

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  14. Show that the points A(1,2,3),\ B(-1,-2,-1),\ C(2,3,2)a n d\ D(4,7,6) ...

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  15. Find the equation of the set of the points P such that is distances fr...

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  16. Given that P(3,2,-4),\ Q(5,4,-6)\ a n d\ R(9,8,-10) are collinear. Fin...

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  17. Three vertices of a parallelogram ABCD are A(3,-1,2),\ B(1,2,-4)a n d\...

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  18. Find the lengths of the medians of the triangle with vertices A(0,0,6)...

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  19. Let A(3,2,0),\ B(5,3,2),\ C(-9,6,-3) be three points forming a triangl...

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  20. If the origin is the centroid of the triangle with vertices P(2a ,\ 2,...

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