Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

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)

98 Views

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.

115 Views

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.

Solution not provided.
Ans. $open parentheses 1 half comma space 1 comma space fraction numerator negative 3 over denominator 2 end fraction close parentheses comma space 1 half square root of 14$

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.

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.

94 Views

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