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If the origin is the centroid of a triangle ABC having vertices `A(a ,1,3),\ B(-2, b ,-5)a n d\ C(4,7, c)` , find the values of `a , b , cdot`

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The correct Answer is:
a=1, b= -2, c = -1
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NAGEEN PRAKASHAN ENGLISH-INTRODUCTION OF THREE DIMENSIONAL GEOMETRY-Exercise 12 C
  1. Find the co-ordinates of a point which divides the line segment joinin...

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  2. If the given points A(3, 3, -4), B(5, 4, -6) and C(9, 8, -10) are coll...

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  3. (i) Find the ratio in which yz-plane divides the join of points (2, 4,...

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  4. Find the ratio in which the line segment having the end points A(-1, -...

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  5. Find the coordinates of the point where the line through (3, 4, 1) and...

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  6. Find the ratio in which the line joining the points (1,2,3)a n d(-3...

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  7. Find the ratio in which the join the A(2,1,5)a n dB(3,4,3) is divided ...

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  8. Find the coordinates of the points which trisect the line segment A ...

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  9. Find the co-ordinates of a point which divides the line segment joinin...

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  10. The co-ordinates of the vertices of a parallelogram ABCD are A(-1,2,3)...

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  11. Show that the points (2,3,4),(-1,-2,1),(5,8,7) are collinear.

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  12. Find the ratio in which the line segment joining the points (2,-1,3) ...

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  13. Find the ratio in which the sphere x^2+y^2+z^2=504 divides the line jo...

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  14. 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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  15. The co-ordinates of two vertices of Delta ABC are A(-5,7,3) and B(7,-6...

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  16. The co-ordinates of two vertices of Delta ABC are A(3,2,-4) and B(-2,3...

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  17. If the origin is the centroid of a triangle ABC having vertices A(a ,1...

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  18. The mid points of the sides of as triangle are (1, 5, -1), (0, 4, -...

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  19. The co-ordinates of two vertices of Delta ABC are A(8,-9,8) and B(1,2,...

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