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Show that the triangle with vertices (0,...

Show that the triangle with vertices (0, 7, 10), (-1, 6, 6) and (- 4, 9, 6) is right-angled.

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Find the area of a triangle whose vertices are ( 1, -1), (- 4, 6) and (-3, -5).

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

Find the lenghts of the medians of the triangle with vertices A(0,0,6), B(0,4,0) and C(6,0,0)

Using vectors, find the area of the triangle having vertices A (2, 5, 6), B (3, 3, 1) and C (4, 6, 3)

Prove that the points (0, 7,-10), (1, 6,-6) and (4,9, - 6) are the vertices of an isosceles triangle.

Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7, -6). Also find the radius of the circumircle.

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MODERN PUBLICATION-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Prove that the following points are collinear : (- 2, 3, 5), (1, 2,...

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  2. Verify that the points (3, - 2, 4), (1, 0, - 2) and (-1,2, - 8) are co...

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  3. Show that the triangle with vertices (0, 7, 10), (-1, 6, 6) and (- 4, ...

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  4. Are the points A (3, 6, 9), B (10, 20, 30) and C (25,- 41, 5) the vert...

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  5. Prove that the points (0, 7,-10), (1, 6,-6) and (4,9, - 6) are the ver...

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  6. Show that A(a,b,c),B(b,c,a) and C(c,a,b) are the vertices of an equila...

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  7. Show that the points : (0,4,1),(2,3,-1),(4,5,0) and (2,6,2) are vertic...

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

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

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

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  11. Find the equation of the set of points P, the sum of whose distance fr...

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

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

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

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  15. Show that (-1, 4, -3) is the circumcentre of the triangle formed by th...

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  16. Find the co-ordinates of the point, which divides the join of (-2, 3, ...

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  17. Find the co-ordinates of the point, which divides the join of (-2, 3, ...

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  18. Find the co-ordinates of the points, which divide the join of the poin...

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  19. Find the co-ordinates of the points, which divide the join of the poin...

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  20. Find the co-ordinates of the mid-point of the join of the points A (3,...

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