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Introduction To Three Dimensional Geometry

Short Answer Type

51. Show that the following sets of points are collinear.
A (6, - 7, - 1), B (2, - 3, 1), C (4, - 5, 0)

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52. Show that the following sets of points are collinear.
A (1, - 1, 3), B (2, - 4, 5), C(5, - 13, 11).

127 Views

53. Show that the following sets of points are collinear.
A (3, - 2, 4), B (1, 0, - 2), C (- 1, 2, - 8)

112 Views

Long Answer Type

54. Show that the points A (0, 1, 2), B (2, - 1, 3) and C (1, - 3, 1) are the vertices of an isosceles right angled triangle.

100 Views

55.

Find the co-ordinates of a point equidistant from four points.
O (0, 0, 0), A (2p, 0, 0), B (0, 2q, 0) and C (0, 0, 2r). Find also the distance.

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56. Find the co-ordinates of a point which is equidistant from four points P (1, 0, 0), Q (0, 2, 0), R (0, 0, - 3) and O (0, 0, 0). Find also the distance.

105 Views

Short Answer Type

57. Find the value of k, so that the distance between points (7, - 3, 1) and (4, k, 5) is 13 units.

102 Views

58. Show that the points A (0, 7 - 10), B (1, 6, - 3) and C (4, 9, - 6) form the vertices of an isosceles triangle.

Solution not provided.

102 Views

59. Show that the points A (2, 3, 4), B (3, 4, 2) and C (4, 2, 3) form the vertices of an equilateral triangle.

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60. Show that the points A (-1, 2, 1), B (1, -2, 5), C (4, - 7, 8) and D (2, - 3, 4) form the vertices of a parallelogram.

119 Views