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If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3), B(-2, b, -5) and C(4, 7, c), Find the values of a, b, c.

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The correct Answer is:
a = -2, b = -8 and c = 2.
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KUMAR PRAKASHAN-INTRODUCTION TO THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. Locate the following points : (i) (1, -1, 3) (ii) (-1, 2, 4) (ii...

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  2. Name the octant in which each of the following points lies. (i) (1, ...

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  3. Let A, B, C be the feet of perpendiculars from a point P on the X, Y, ...

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  4. Let A, B, C be the feet of perpendiculars from a point P on the X, Y, ...

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  5. How far apart are the points (2, 0, 0) and (-3, 0, 0) ?

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  6. Find the distance from the origin to A(6, 6, 7).

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  7. Show that if x^(2)+y^(2)=1, then the point (x,y,sqrt(1-x^(2)-y^(2))) i...

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  8. Show that the point A(1, -1, 3), B(2, -4, 5) and C(5, -13, 11) are col...

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  9. Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(...

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  10. Show that the triangle ABC with vertices A(0, 4, 1), B(2, 3, -1) and C...

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  11. Find the centroid of the triangle whose vertices are (3, -5), (-7, 4) ...

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  12. Find the centroid of a triangle, the mid-point of whose sides are D(1,...

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  13. The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5) an...

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  14. Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(...

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  15. Find the coordinate of the points which trisect the line segment joini...

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

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  17. If A(2, 2, -3), B(5, 6, 9) and C(2, 7, 9) be the vertices of a triangl...

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