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Verify the following: (-1,2,1), (1,-2,5)...

Verify the following: (-1,2,1), (1,-2,5), (4,-7,8) and (2,-3,4) are vertices of a parallelogram.

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To verify that the points (-1, 2, 1), (1, -2, 5), (4, -7, 8), and (2, -3, 4) are the vertices of a parallelogram, we will follow these steps: ### Step 1: Assign the Points Let: - A = (-1, 2, 1) - B = (1, -2, 5) - C = (4, -7, 8) - D = (2, -3, 4) ...
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RD SHARMA-INTRODUCTIONS TO 3-D COORDINATE GEOMETRY-Solved Examples And Exercises
  1. Verify the following: (0,7,-10), (1,6,-6) and (4,9,-6) are vertices of...

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  2. Verify the following: (0,7,10), (-1,6,6) and (-4,9,6) are vertices of ...

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  3. Verify the following: (-1,2,1), (1,-2,5), (4,-7,8) and (2,-3,4) are ...

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  4. Verify the following: (5,-1,1),(7,-4,7), (1,-6,10) and (-1,-3,4) are ...

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  5. Find the locus of the points which are equidistant from the points ...

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  6. Find the locus of the point, the sum of whose distances from the point...

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  7. 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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  8. Find the equation of the set of the points P such that is distances fr...

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

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  10. Three vertices of a parallelogram ABCD are A(3,-1,2),\ B(1,2,-4)a n d\...

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  11. Find the lengths of the medians of the triangle with vertices A(0,0,6)...

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  12. Let A(3,2,0),\ B(5, 3,2),\ C(-9,6,-3) be three points forming a triang...

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  13. If the origin is the centroid of the triangle with vertices P(2a ,\ 2,...

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  14. A point R with x-coordinates 4 lies on the line segment joining the po...

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  15. Show that the coordinates off the centroid of the triangle with ver...

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  16. Let P\ a n d\ Q be any two points. Find the coordinates of the point R...

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  17. The vertices f the triangle are A(5,4,6),\ B(1,-1,3)n a d\ C(4,3,2)dot...

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  18. A point C with z-coordinate 8 lies on the line segment joining the ...

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  19. Show that the three points A(2,3,4),\ B(-1,2,-3)a n d\ C(-4,1,-10) are...

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  20. Find the ratio in which the line joining (2,4,5) and (3,5,4) is divide...

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