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

71. Find the co-ordinates of the point which divides the line segment formed by joining the points (- 2, 3, 5) and (1, -4, 6) in the ratio of 2 : 3 externally.

117 Views

72. Given that P (3, 2, -4), Q (5, 4, -6) and R (9, 8, -10) are collinear. Find the ratio in which Q divides PR.

Let point Q (5, 4, - 6) divides the join of P (3, 2, - 4) and R (9, 8, - 10) in the ratio k : 1.
For point Q,

straight x equals fraction numerator 9 straight k plus 3 over denominator straight k plus 1 end fraction equals 5

(given)

rightwards double arrow

9 straight k plus 3 equals 5 straight k plus 5 space rightwards double arrow space 4 straight k space equals space 2 space rightwards double arrow space straight k equals 1 half

straight y equals fraction numerator 8 straight k plus 2 over denominator straight k plus 1 end fraction equals fraction numerator 8 open parentheses begin display style 1 half end style close parentheses plus 2 over denominator begin display style 1 half end style plus 1 end fraction equals fraction numerator 6 over denominator begin display style 3 over 2 end style end fraction equals 4

space space space straight z equals fraction numerator negative 10 straight k minus 4 over denominator straight k plus 1 end fraction equals fraction numerator negative 10 open parentheses begin display style 1 half end style close parentheses minus 4 over denominator begin display style 1 half plus 1 end style end fraction equals negative 6

which give us point Q (5, 4, -6)
Hence, Q divides PR in the ratio

1 half colon 1 space or space 1 colon 2

internally.

176 Views

73. Using section formula, prove that the three points (-4, 6, 10), (2, 4, 6) and (14, 0, - 2) are collinear. Also find the ratio in which point B divides the join of A and C.

719 Views

74. Find the co-ordinates of the points of trisection of the line segment joining the points P (3, 2, - 1) and Q (1, 2, 5).

125 Views

75.

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

400 Views

76.

Find the ratio in which the join of P (2, 1, -1) and Q (3, 2, 4) is divided by XY-plane.

120 Views

77. A point R with x-coordinate 4 lies on the line joining the points P (2, - 3, 4) and Q (8, 0, 10). Find the co-ordinates of point R.

117 Views

Long Answer Type

78. Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0).

168 Views

Short Answer Type

79. A (3, 2, 0), B (5, 3, 2) and C (-9, 6, -3) are the vertices of a triangle ABC. The bisector AD of ∆ BAC meets BC at D. Find the co-ordinates of D.

1213 Views

80. The co-ordinates of the mid-point C of a line segment AB are (-1, -2, 1). If the co-ordinates of point A are (2, 1, -3), find the co-ordinates of B.

93 Views