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Show that the points (3, 1, 4), (6, 4, 4...

Show that the points (3, 1, 4), (6, 4, 4), (8, 2, 4) and (5, -1, 4) are the vertices of a rectangle.
[Hint : Opposite sides and diagonals of rectangle are equal.]

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AAKASH INSTITUTE ENGLISH-THREE DIMENSIONAL GEOMETRY -TRY YOURSELF
  1. Find the equation of the locus of point P, the sum of whose distance f...

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  2. Show that the points (3, -1, 2), (5, -2, -3), (-2, 4, 1) and (-4, 5, 6...

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  3. Show that the points (3, 1, 4), (6, 4, 4), (8, 2, 4) and (5, -1, 4) ar...

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  4. Find the coordinates of the point which divides the line segment join...

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  5. Find the coordinates of the point which divies the line segment joinin...

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  6. Find the coordinates of the points which trisect the line segment join...

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  7. Find the coordinates of the points of the line segment joining (1, 3,...

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  8. Three vertices of a parallelogram are (1, 2, 1), (2, 5, 6) and (1, 6, ...

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  9. Three vertices of a parallelogram are (0, 0, 0), (2, -1, 2) and (5, 6,...

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

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  11. Find the ratio in which the line joining the points (2, 3, 5) and (3, ...

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  12. Using section formula, show that the points A(1, 2, 1), B(2, 1, 0) and...

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  13. Using section formaul, show that the points (2, -1, 3), (0, 1, 2) and ...

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  14. A point with x-coordinate 9 lies on the line segment joining the point...

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  15. A point with z-coordinate 6 lies on the line segment joining the poin...

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  16. Find the coor dinates of the centrod of a triangle whose coordinates a...

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  17. If (1, 1, 1) is the centroid of the triangle with vertices (2a, 3, 7),...

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  18. The mid-points of the sides of a triangle are given by (3, 2, -4), (9,...

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  19. The mid-points of the sides of a triangle ABC are given by A(0, 0, 0),...

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  20. If P has coordinates (5, 4, -9). What is length OP and it's direction ...

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