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

Show that the points (-3, 2, 4), (-1, 5, 9) and (1, 8, 14) lie on a line.
[Hint : Sum of any two sides is equal to third side.]

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Show that the points (2, -3, 3), (1, 2, 4) and (3, -8, 2) are collinear. [Hint : Sum of any two sides is equal to third side.]

Show that the points (-1, 0, -4), (0, 1, -6) and (1, 2, -5) from a right angled triangle. [Hint : Sum of squares of any two sides is equal to the square of third side.]

Using distance formula show that the points A(-3,2,4),B(-1,5,9) and C(1,8,14) are collinear

Show that the points (9, -2), (-5, 12) and (-7, 10) lie on that circle whose centre is the point (1, 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.]

Show that the points (a+5,a-4),(a-2,a+3) and (a,a) do not lie on a straight line of any value of a .

Show that the points A(-1,4,-3),B(3,2,-5),C(-3,8,-5) and D(-3,2,1) are coplanar.

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

Sum of any two sides of a triangle is greater than the third side.

AAKASH INSTITUTE-THREE DIMENSIONAL GEOMETRY -TRY YOURSELF
  1. Show that the points (-1, 0, -4), (0, 1, -6) and (1, 2, -5) from a rig...

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

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  3. Show that the points (-3, 2, 4), (-1, 5, 9) and (1, 8, 14) lie on a li...

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  4. Show that the points (2, -3, 3), (1, 2, 4) and (3, -8, 2) are collinea...

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  5. Find the equation of the locus of point P, the sum of the square of wh...

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  6. Find the equation of the locus of point P, the sum of whose distance f...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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