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Given that P(3,2,-4),\ Q(5,4,-6)\ a n d\...

Given that `P(3,2,-4),\ Q(5,4,-6)\ a n d\ R(9,8,-10)` are collinear. Find the ratio in which `Q` divides `P Rdot`

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To find the ratio in which point Q divides the line segment PR, we can use the section formula in 3D coordinate geometry. ### Step-by-Step Solution: 1. **Identify the coordinates of points P, Q, and R:** - \( P(3, 2, -4) \) - \( Q(5, 4, -6) \) - \( R(9, 8, -10) \) ...
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RD SHARMA-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-Solved Examples And Exercises
  1. 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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  2. Find the equation of the set of the points P such that is distances fr...

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

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

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

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

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

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  8. A point R with x-coordinates 4 lies on the line segment joining the po...

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  9. Show that the coordinates off the centroid of the triangle with ver...

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  10. Let P\ a n d\ Q be any two points. Find the coordinates of the point R...

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  11. The vertices f the triangle are A(5,4,6),\ B(1,-1,3)n a d\ C(4,3,2)dot...

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  12. A point C with z-coordinate 8 lies on the line segment joining the ...

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  13. Show that the three points A(2,3,4),\ B(-1,2,-3)a n d\ C(-4,1,-10) are...

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  14. Find the ratio in which the line joining (2,4,5) and (3,5,4) is divide...

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

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  16. If the points A(3,2,-4),\ B(9,8,-10)a n d\ C(5,4,-6) are collinear, fi...

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  17. The id points of the sides of a triangle ABC are given by (-2,3,5),(4,...

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  18. Find the ratio in which the sphere x^2+y^2+z^2=504 divides the line jo...

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  19. Find the centroid of a triangle, mid points of whose sides are (1,2...

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  20. The centroid of a triangle ABC is at the point (1,1,1). If the coor...

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