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If the vertices of a parallelogram ABCD ...

If the vertices of a parallelogram ABCD are A ( 1,2,3) . B ( -1,-2,-1) and C (2,3,2) then find the fourth vertex D.

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To find the fourth vertex \( D \) of the parallelogram \( ABCD \) given the vertices \( A(1, 2, 3) \), \( B(-1, -2, -1) \), and \( C(2, 3, 2) \), we can use the property that the diagonals of a parallelogram bisect each other. ### Step-by-step solution: 1. **Identify the coordinates of the known vertices**: - \( A(1, 2, 3) \) - \( B(-1, -2, -1) \) - \( C(2, 3, 2) \) ...
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NCERT EXEMPLAR-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-Fillers
  1. If the vertices of a parallelogram ABCD are A ( 1,2,3) . B ( -1,-2,-1)...

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  2. The three axes OX, OY and OZ determine ………….

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  3. The three planes, determine a rectangular parallelopiped which has ………...

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  4. The coordiantes of a point are the perpendicular distance from the ….....

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  5. The Three coordiantes planes divide the space into ……. Parts.

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  6. If a point P lies in YZ- plane , the n the coordinates of a point on Y...

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  7. The equation of YZ- plane is ………

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  8. If the point P lies on Z - axis , then coordinates of p are of the for...

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  9. The equation of Z - axis , are…………..

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  10. A line is parallel to XY- plane if all the points on the line have equ...

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  11. A line is parallel to X-axis,if all the points on the line have equal…...

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  12. 45x=a represent a plane parallel to ………..

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  13. The plane parallel to YZ- plane is perpendicular to ………….

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  14. The length of the longest piece of a string that can be stetched strai...

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

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

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  17. Match each item given under the column I to its correct answer given u...

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