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suppose that the mid point of the sides BC,CA and AB of a triangle `Delta ABC` are (5,7,11), (0,8,5) and (2,3,-1)
If the vertices of the triangle are `A(x_1,y_1,z_1), B(x_2,y_2,z_2) and C(x_3,y_3,z_3)` derive nine equations in `x_1,x_2,x_3,y_1,y_2,y_3,z_1,z_2, and z_3`

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`x_2+x_3=10, y_2+y_3=14, z_2+z_3=22, x_1+x_3=0, y_1+y_3=16, z_1+z_3=10, x_1+x_2=4, y_1+y_2=6, z_1+z_2=2`
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A N EXCEL PUBLICATION-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Consider the points A(-5,6,8), B(1,8,11),C(4,2,9) and D(-2,0,6). Find...

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  2. Consider the points A(-5,6,8), B(1,8,11),C(4,2,9) and D(-2,0,6) Find...

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  3. Let A (2,3,5), B(-1,5,-1) and C(4,-3,2) be the vertices of a DeltaABC ...

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  4. Let A (2,3,5), B(-1,5,-1) and C(4,-3,2) be the vertices of a DeltaABC ...

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  5. Consider the points A(2,-3,0) and B (-1,1,c) Find the distance betwe...

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  6. Consider the points A(2,-3,0) and B (-1,1,c) If the distance is 13 u...

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  7. Consider the point A(3,2,-4) and B (9,8,-10) Find the co-ordinates o...

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  8. Consider the point A(3,2,-4) and B (9,8,-10) Find the co-ordinates o...

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  9. suppose that the mid point of the sides BC,CA and AB of a triangle Del...

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  10. Suppose that the midpoints of the sides BC,CA and AB of a triangle ABC...

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  11. Given the vertices A(2,-1,4), B(3,2,-6) and C(-5,0,2) of a triangle AB...

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  12. Given the vertices A(2,-1,4), B(3,2,-6) and C(-5,0,2) of a triangle AB...

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  13. Given the points P(1,-1,3), Q(2,-4,5) and R(5,-13,11) Prove that P,Q...

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  14. Given the points P(1,-1,3), Q(2,-4,5) and R(5,-13,11) Find the ratio...

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  15. The vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,-4) and C(-1...

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

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  17. If the origin is the centroid of the triangle PQR with vertices P(2a,2...

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  18. Find the co-ordinates of a point on y-axis which are at a distance of ...

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  19. A point R with x-coordinate 4 lies on the line segment joining the poi...

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  20. If A and B are the points (3,4,5) and (-1,3,-7) respectively, find the...

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