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In what ratio does the origin divides th...

In what ratio does the origin divides the line segment joining the points P(-1,-2,-3) and Q(4,8,12).

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To find the ratio in which the origin divides the line segment joining the points P(-1, -2, -3) and Q(4, 8, 12), we can use the section formula in three dimensions. ### Step-by-Step Solution: 1. **Identify the Points**: Let \( P(-1, -2, -3) \) and \( Q(4, 8, 12) \) be the two points. 2. **Let the Ratio be k:1**: ...
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MAHAVEER PUBLICATION-CO-ORDINATE GEOMETRY OF THREE DIMENSIONS-QUESTION BANK
  1. A point moves in such a way that its distance from the X-axis is twice...

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  2. Find the co-ordinates of the point which divides the join of (5,8,-3) ...

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  3. In what ratio does the origin divides the line segment joining the poi...

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  4. Find the co-ordinates of the centroid of the triangle whose vertices a...

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  5. Find the point of intersection of the medians of the triangle whose ve...

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  6. Find the lengths of the medians of the triangle whose vertices are A(2...

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  7. Can there be any line which makes angles 30^@,45^@ and 60^@ with the c...

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  8. If a line makes angles 60^@ and 135^@ respectively with x and y axes f...

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  9. If a line makes angles alpha, beta and gamma with the co-ordinate axes...

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  10. Find the direction cosines of the line whose direction ratio are 2,-4,...

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  11. Find the direction cosines of the line whose direction ratio are sqrt3...

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  12. Find the direction cosines of the line whose direction ratio are a-b,b...

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  13. If a line make angle 30^@ and 60^@ with the x and y axes, what angles ...

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  14. Find the direction ratios and direction cosines of the lines joining t...

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  15. Find the direction ratios and direction cosines of the lines joining t...

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  16. Find the angle between the following pair of lines whose direction rat...

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  17. Find the angle between the following pair of lines whose direction rat...

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  18. Show that the line joining the points (1,2,3) and (4,5,7) is parallel ...

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  19. For what value of x will the line joining the points (x,6,-3),(5,3,2)w...

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  20. A (6,3,2),B(4,1,4),C(3,-4,7) and D(0,2,5) are four given points. Find ...

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