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Show that the points A(1,2,3),\ B(-1,-2,...

Show that the points `A(1,2,3),\ B(-1,-2,-1),\ C(2,3,2)a n d\ D(4,7,6)` are the vertices of a parallelogram ABCD but not a rectangle.

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NAGEEN PRAKASHAN-INTRODUCTION OF THREE DIMENSIONAL GEOMETRY-Exercise 12 B
  1. Find the distance between the following pairs of points : (i) (-2, 1...

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  2. Show that the following points are collinear : (i) (0,7,-7), (1,4,-5...

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  3. Show that the points (0,7,10), (-1,6,6) and(-4,9,6) are the vertices o...

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  4. Show that the points (-4,-4,-1),(0,2,3) and (4,6,-3) are the vertices ...

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  5. Show that the points (-2,4,1),(-1,5,5),(2,2,5) and (1,1,1) are the ver...

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  6. Prove that the point A(1,3,0),\ B(-5,5,2),\ C(-9,-1,2)\ a n d\ D(-3,-3...

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  7. Show that the points A(1,3,4),\ B(-1,6, 10),\ C(-7,4,7)a n d\ D(-5,1,1...

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  8. Show that the points A(3,3,3,),\ B(0,6,3),\ C(1,7,7)a n d\ D(4,4,7) ar...

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  9. 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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  10. Show that the points (2,-1,3), (0,1,2) and (1,-3,1) are the vertices o...

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  11. Determine the points in i. xy-plan e ii. yz-plane and iii zx-plane ...

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  12. Find a point on Z-axis which is equidistant from the points (1,5,7) an...

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  13. Find the points on z-axis which are at a distance sqrt21 from the po...

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  14. If A(-2,2,3)a n dB(13 ,-3,13) are two points. Find the locus of a poin...

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  15. If A(3,4,1) and B(-1,2,3) are two points, then find the locus of a mov...

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  16. Find the point which equisdistant from points O(0,0,0),A(a,0,0)B (0,b,...

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  17. Find the locus of a point whiich moves in such a way that the sum of i...

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  18. A moving point 'P' moves such that AP^(2)+BP^(2)=10 where the co-ordin...

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