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If the distance between the points (x,2,...

If the distance between the points (x,2,0) and (1,3,1) be `sqrt6` , find the value of x.

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To find the value of \( x \) given that the distance between the points \( (x, 2, 0) \) and \( (1, 3, 1) \) is \( \sqrt{6} \), we can follow these steps: ### Step 1: Use the Distance Formula The distance \( d \) between two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) in three-dimensional space is given by the formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \] In our case, we have: ...
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MAHAVEER PUBLICATION-CO-ORDINATE GEOMETRY OF THREE DIMENSIONS-QUESTION BANK
  1. Find the distances between the following pair of points. (4,3,-6) and ...

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  2. Find the distances between the following pair of points. (-4,-2,3) and...

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  3. If the distance between the points (x,2,0) and (1,3,1) be sqrt6 , find...

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

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  5. Show that the triangle with vertices (6,10,10),(1,0,-5) and (6,-10,0)...

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  6. Find the locus of the point which is equidistant from the points (1,-2...

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  7. The distance of a point from the x-axis is twice its distance from the...

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  8. A point moves in such a way that its distance from the X-axis is twice...

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

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

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

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

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

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

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

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

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

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

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

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

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