3D-PART-I-03-ASSIGNMENT

1. From which of the following the distance of the point (1,2,3) is (a) Origin (b) x-axis (c) y-axis (d) z-axis 2. If be the points, then the distance AB is (a) (b) (c) (d) None of these 3. Perpendicular distance of the point (3,4,5) from the y-axis, is (a) (b) (c) 4 (d) 5 4. Distance between the points (1,3,2) and (2,1,3) is (a) 12 (b) (c) (d) 6 5. The shortest distance of the point (a,b,c) from the x-axis is (a) (b) (c) (d) 6. Points (1,1,1), and (2,2,5) are the vertices of (a) Rectangle (b) Square (c) Parallelogram (d) Trapezium 7. The triangle formed by the points (0,7,10), (–1,6,6) (–4,9,6) is (a) Equilateral (b) Isosceles (c) Right angled (d) Right angled isosceles 8. The points ; and are vertices of a (a) Square (b) Rhombus (c) Rectangle (d) None of these 9. The coordinates of a point which is equidistant from the points (0,0,0), (a,0,0), (0,b,0) and (0,0,c) are given by (a) (b) (c) (d) 10. If and are given, then the coordinates of P which divides AB externally in the ratio , are (a) (b) (c) (d) None of these 11. The coordinates of the point which divides the join of the points and (4,3,1) in the ratio internally are given by (a) (b) (c) (d) 12. Points (–2, 4, 7), (3, –6, –8) and (1, ¬–2, –2) are (a) Collinear (b) Vertices of an equilateral triangle (c) Vertices of an isosceles triangle (d) None of these 13. Which of the following set of points are non-collinear (a) (1, –1, 1), (–1, 1, 1), (0, 0, 1) (b) (1, 2, 3), (3, 2, 1), (2, 2, 2) (c) (–2, 4, –3), (4, –3, –2), (–3, –2, 4) (d) (2, 0, –1), (3, 2, –2), (5, 6, –4) 14. If the points (–1, 3, 2), (–4, 2, –2) and (5, 5, ) are collinear, then (a) –10 (b) 5 (c) –5 (d) 10 15. The area of triangle whose vertices are (1, 2, 3), (2, 5, –1) and (–1, 1, 2) is (a) 150 sq. units (b) 145 sq. units (c) (d) 16. Volume of a tetrahedron is K (area of one face) (length of perpendicular from the opposite vertex upon it), where K is (a) (b) (c) (d) 17. A point moves so that the sum of its distances from the points and remains 10. The locus of the point is (a) (b) (c) (d) 18. If the sum of the squares of the distances of a point from the three coordinate axes be 36, then its distance from the origin is (a) 6 (b) (c) (d) None of these 19. All the points on the x-axis have (a) (b) (c) (d) 20. The equations in xyz space represent (a) Cube (b) Rhombus (c) Sphere of radius p (d) Point (p,p,p) 21. The orthocentre of the triangle with vertices (1,2,3), (2,3,1) and (3,1,2) is (a) (1, 1, 1) (b) (2, 2, 2) (c) (6, 6, 6) (d) None of these 22. If , then circumcentre of the triangle with vertices (a,b,c); (b,c,a) and (c,a,b) is (a) (b) ( ) (c) ( ) (d) None of these 23. are two vertices of . If its centroid be , then its third vertex is (a) (b) (c) (d) None of these 24. If points (2, 3, 4), (5, a, 6) and (7, 8, b) are collinear, then values of a and b are (a) (b) (c) (d) 25. If a line makes angles of 30° and 45° with x-axis and y-axis, then the angle made by it with z-axis is (a) 45° (b) 60° (c) 120° (d) None of these 26. If a straight line in space is equally inclined to the coordinate axes, the cosine of its angle of inclination to any one of the axes is (a) (b) (c) (d) 27. If the length of a vector be 21 and direction ratios be 2, –3, 6, then its direction cosines are (a) (b) (c) (d) None of these 28. If O is the origin, with d.r.‘s then the co-ordinates of P are (a) (b) (1, 2, 2) (c) (d) (3, 6, – 9) 29. The numbers 3, 4, 5 can be (a) Direction cosines of a line (b) Direction ratios of a line in space (c) Coordinates of a point on the plane (d) Co-ordinates of a point on the plane 30. If l, m, n are the d.c.'s of a line, then (a) (b) (c) (d) 31. If a line lies in the octant OXYZ and it makes equal angles with the axes, then (a) (b) (c) (d) 32. If a line makes equal angle with axes, then its direction ratios will be (a) 1, 2, 3 (b) 3, 1, 2 (c) 3, 2, 1 (d) 1, 1, 1 33. The coordinates of the point P are (x, y, z) and the direction cosines of the line OP, when O is the origin, are l, m, n. If OP = r, then (a) (b) (c) (d) None of these 34. The direction ratios of the diagonals of a cube which joins the origin to the opposite corner are (when the 3 concurrent edges of the cube are coordinate axes) (a) (b) –1, 1, –1 (c) 2, –2, 1 (d) 1, 2, 3 35. If the direction ratios of a line are 1, –3, 2, then the direction cosines of the line are (a) (b) (c) (d) 36. If a line make with the positive direction of x, y and z-axis respectively. Then is (a) 1/2 (b) –1/2 (c) –1 (d) 1 37. The direction-cosines of the line joining the points (4, 3, –5) and (–2, 1, –8) are (a) (b) (c) (d) None of these 38. The direction ratios of the line joining the points (4, 3, –5) and (–2, 1, –8) are (a) (b) 6, 2, 3 (c) 2, 4, –13 (d) None of these 39. The coordinates of a point P are (3, 12, 4) with respect to origin O, then the direction cosines of OP are (a) 3, 12, 4 (b) (c) (d) 40. The direction cosines of a line segment AB are . If and the coordinates of A are (3, ¬–6, 10), then the coordinates of B are (a) (1, –2, 4) (b) (2, 5, 8) (c) (–1, 3, –8) (d) (1, –3, 8) 41. If are the direction cosines of a line, then the value of n is (a) (b) (c) (d) 42. If a line makes the angle with three dimensional coordinate axes respectively, then (a) –2 (b) –1 (c) 1 (d) 2 43. A line makes angles of 45° and 60o with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z, is (a) 30° or 60° (b) 60° or 90° (c) 90° or 120° (d) 60° or 120° 44. If be the angles which a line makes with the positive direction of coordinate axes, then (a) 2 (b) 1 (c) 3 (d) 0 45. A line makes angles with the coordinate axes. If , then (a) 0o (b) 90° (c) 180° (d) None of these 46. The coordinates of the points P and Q are and respectively, then the projection of the line PQ on the line whose direction cosines are l, m, n, will be (a) (b) (c) (d) 47. The projection of the line segment joining the points (–1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3, is (a) 10/7 (b) 22/7 (c) 18/7 (d) None of these 48. The projection of any line on coordinate axes be respectively 3, 4, 5, then its length is (a) 12 (b) 50 (c) (d) None of these 49. If is the angle between the lines AB and CD, then projection of line segment AB on line CD is (a) (b) (c) (d) 50. The projections of a line on the co-ordinate axes are 4, 6, 12. The direction cosines of the line are (a) (b) 2, 3, 6 (c) (d) None of these 51. The projections of segment PQ on the coordinate planes are –9, 12, –8 respectively. The direction cosines of PQ are (a) (b) (c) (d) 52. The projections of a line segment on axes are 12, 4, 3. The length and the direction cosines of the line segments are (a) (b) (c) (d) None of these 53. The coordinates of A and B be (1, 2, 3) and (7, 8, 7), then the projections of the line segment AB on the coordinate axes are (a) 6, 6, 4 (b) 4, 6, 4 (c) 3, 3, 2 (d) 2, 3, 2 54. A line segment (vector) has length 21 and direction ratios (2, –3, 6). If the line makes an obtuse angle with x-axis, the components of the line (vector) are (a) 6, –9, 18 (b) 2, –3, 6 (c) –18, 27, –54 (d) –6, 9, –18 55. The angle between the pair of lines with direction ratios (1, 1, 2) and is (a) 30° (b) 45° (c) 60° (d) 90° 56. The angle between a line with direction ratios and a line joining (3, 1, 4) to (7, 2, 12) is (a) (b) (c) (d) None of these 57. The angle between the lines whose direction cosines are proportional to (1, 2, 1) and (2, –3, 6) is (a) (b) (c) (d) 58. If the vertices of a triangle are A (1, 4, 2), B(–2, 1, 2), C(2, –3, 4), then the angle B is equal to (a) (b) (c) (d) 59. If the coordinates of the points P, Q, R, S be ( 1, 2, 3), ( 4, 5, 7), ( –4, 3, –6) and ( 2, 0, 2) respectively, then (a) (b) (c) (d) None of these 60. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (–4, 3, –6) and (2, 9, 2) respectively, then the angle between the lines AB and CD is (a) (b) (c) (d) None of these 61. If the angle between the lines whose direction ratios are and be 45°, then (a) 1 (b) 2 (c) 3 (d) 4 62. If O be the origin and and be two points such that , then (a) 2 (b) –2 (c) No such real b exists (d) None of these 63. If d.r.'s of two straight lines are 5, –12, 13 and –3, 4, 5 then, angle between them is (a) (b) (c) (d) 64. If direction ratio of two lines are and then these lines are parallel if and only if (a) (b) (c) (d) None of these 65. If and be such that the line , then the value of k will be (a) 1 (b) 2 (c) 3 (d) 0 66. and are the vertices of a right angled isosceles triangle. If , then (a) 0 (b) 2 (c) –1 (d) –3 67. The angle between two diagonals of a cube will be (a) (b) (c) Constant (d) Variable 68. If a line makes angles with the four diagonals of a cube, then the value of (a) 1 (b) (c) Constant (d) Variable 69. The angle between the lines whose direction cosines satisfy the equations is given by (a) (b) (c) (d) 70. If three mutually perpendicular lines have direction cosines and then the line having direction cosines and make an angle of ……….with each other (a) 0° (b) 30° (c) 60° (d) 90° 71. The straight lines whose direction cosines are given by are perpendicular, if (a) (b) (c) (d) 72. The angle between the lines whose direction cosines are connected by the relations and , is (a) (b) (c) (d) None of these 73. are three points forming a triangle and AD is the bisector of the , then coordinates of D are (a) (b) (c) (d) 74. The direction cosines of two lines at right angles are and . Then the d.c. of a line to both the given lines are (a) (b) (c) (d) None of these 75. Three lines drawn from origin with direction cosines are coplanar iff , since (a) All lines pass through origin (b) It is possible to find a line perpendicular to all these lines (c) Intersecting lines are coplanar (d) None of these 76. The direction cosines of a variable line in two adjacent positions are and . If angle between these two positions is , where is a small angle, then is equal to (a) (b) (c) (d) None of these 77. If direction cosines of two lines OA and OB are respectively proportional to 1, –2, –1 and 3, –2, 3 then direction cosine of line perpendicular to given both lines are (a) (b) (c) (d) None of these 78. A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the d.r'.s of the normal to the plane are 1, –1, 1, then d.c'.s of the reflected ray are (a) (b) (c) (d) 79. The equation of straight line passing through the point and parallel to z-axis, is (a) (b) (c) (d) 80. Equation of x-axis is (a) (b) (c) (d) 81. The equation of straight line passing through the points (a, b, c) and , is (a) (b) (c) (d) 82. The equation of a line passing through the point (–3, 2, –4) and equally inclined to the axes, are (a) (b) (c) (d) None of these 83. The straight line through (a, b, c) and parallel to x-axis are (a) (b) (c) (d) 84. Equation of the line passing through the point and parallel to the line is given by (a) (b) , where 12l+4m+5n=0 (c) (d) None of these 85. Let G be the centroid of the triangle formed by the points (1, 2, 0), (2, 1, 1), (0, 0, 2). Then equation of the line OG is given by (a) (b) (c) (d) None of these 86. The direction cosines of the line are (a) (b) (c) (d) 87. The direction cosines of the line are (a) (b) (c) 1, 1, 1 (d) None of these 88. The direction ratio's of the line are (a) 3, 1, –2 (b) 2, –4, 1 (c) (d) 89. The angle between two lines and is (a) (b) (c) (d) 90. The angle between the lines and is (a) (b) (c) (d) None of these 91. The angle between the lines and is (a) (b) (c) (d) 92. The value of for which the lines and are perpendicular to each other is (a) 0 (b) 1 (c) –1 (d) None of these 93. The angle between the straight lines and is (a) 45° (b) 30° (c) 60° (d) 90° 94. The angle between the lines and , is (a) 0° (b) 30° (c) 45° (d) 90° 95. The angle between the lines and and is (a) 90° (b) 30° (c) 60° (d) 0° 96. The straight line is (a) Parallel to x-axis (b) Parallel to y-axis (c) Parallel to z-axis (d) Perpendicular to z-axis 97. The lines and are (a) Parallel (b) Skew (c) Coincident (d) Perpendicular 98. The straight lines and are (a) Parallel lines (b) Intersecting at 60° (c) Skew lines (d) Intersecting at right angle 99. The angle between the lines and is (a) (b) (c) (d) None of these 100. The lines and are (a) Parallel (b) Intersecting (c) Skew (d) Coincident 101. The lines and are (a) Parallel (b) Intersecting (c) Skew (d) Perpendicular 102. Lines and are parallel iff (a) is parallel to (b) is parallel to (c) for some real (d) None of these 103. The equation of the line passing through the points and (a) (b) (c) (d) None of these 104. The vector equation of the line joining the points and is (a) (b) (c) (d) 105. The acute angle between the line joining the points and a line parallel to through the point is (a) (b) (c) (d) 106. The shortest distance between the lines and is (a) (b) (c) (d) 107. Shortest distance between lines and is (a) 108 (b) 9 (c) 27 (d) None of these 108. The lines and intersect. The shortest distance between them is (a) Positive (b) Zero (c) Negative (d) Infinity 109. The shortest distance between two straight lines given by and is (a) (b) (c) (d) None of these 110. The shortest distance between the lines and (t and s being parameters) is (a) (b) (c) 4 (d) 3 111. The equation of the line passing through the point (1, 2, –4) and perpendicular to the two lines and , will be (a) (b) (c) (d) None of these 112. The equation of straight line ; in the symmetrical form is (a) (b) (c) (d) None of these 113. The point of intersection of lines and is (a) (b) (c) (d) 114. The length and foot of the perpendicular from the point to the line are (a) (b) (c) (d) None of these