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If the points A(3,2,-4),\ B(9,8,-10)a n ...

If the points `A(3,2,-4),\ B(9,8,-10)a n d\ C(5,4,-6)` are collinear, find the ratio in which C divides AB.

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To find the ratio in which point C divides the line segment AB, we can use the section formula in 3D coordinate geometry. The points given are: - A(3, 2, -4) - B(9, 8, -10) - C(5, 4, -6) ### Step 1: Set up the section formula The section formula states that if a point C divides the line segment AB in the ratio \( m:n \), then the coordinates of C can be expressed as: ...
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RD SHARMA-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-Solved Examples And Exercises
  1. Find the ratio in which the line joining (2,4,5) and (3,5,4) is divide...

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

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

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

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

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

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  8. Find the coordinates of the points which tisect the line segment jo...

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  9. Using section formula, show that the points A(2,-3,4),\ B(-1,2,1)\ a n...

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

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  11. Find the ratio in which the segment joining the points (4,8,10) and ...

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  12. Write the distance of the point P(2,3,5) from the xy-plane.

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  13. Write the distance of the point P(3,4,5) from z-axis.

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  14. If the distance between the points P(a ,2,1)a n d\ Q(1,-1,1) is 5 unit...

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  15. The coordinates of the mid points of sides AB, BC and CA of A B C are...

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  16. Write the coordinates of the foot of the perpendicular from the point ...

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  17. Write the length of the perpendicular drawn from the point P(3,5, 12) ...

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  18. Write the coordinates of third vertex of a triangle having centroid at...

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  19. What is the locus of a point (x , y , z) for which y=0, z=0?

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  20. Find the ratio in which the line segment joining the points (2,4,5) an...

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