81.Find the co-ordinates of the centroid of triangle whose vertices are A (2, 3, -1), B (1, 3, -2) and C (3, 0, 3).
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82.The centroid of a triangle ABC is at the point (1, 1, 1). If the co-ordinates of A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the co-ordinates of the point C
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83.If the origin is the centroid of triangle PQR, with vertices P(2a, 2, 6), Q(- 4, 3b, - 10) and R(8, 14, 2c). Find the values of a, b and c.
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84.Without using distance formula, show that A (-1, 2, 1), B (1, -2, 5) C (4, - 7, 8) and D (2, - 3, 4) are the vertices of a parallelogram ABCD.
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85.Three vertices of a parallelogram ABCD are A (3, -1, 2), B (1, 2, -4), and C (-1, 1, 2). Find the co-ordinates of the fourth vertex.
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Long Answer Type
86.The co-ordinates of the mid-points of sides BC, CA and AB of ∆ ABC are (2, 1, -1), (3, 2, 4) and (1, -2, 3) respectively. Find the co-ordinates of vertices A, B and C.
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Short Answer Type
87.Find the co-ordinates of a point P which divides the join of A (1, - 2, -1) and (1, 5, -8) internally in ratio 3 : 4.
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88.Find the co-ordinates of a point which divides the line joining points A (2, - 1, 3) and B (1, 4, 2) externally in ratio 2 : 3.
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89.Find the ratio in which the line joining points A (2, 4, - 3) and B (-3, 5, 2) is divided to XY-plane.
Short Answer Type
Long Answer Type
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