MathsMaths QuestionsThree Dimensional Geometry Part 1 Questions for CBSE Class 11th

Three Dimensional Geometry Part 1 Questions for CBSE Class 11th

  1. Let A (1, –1, 3), B (2, 3, 5) is divided by P in the ratio 3:4 internally then harmonic conjugate of P w.r.t. to A, B is
  2. The co-ordinates of the point where the line through the points A ( 3 , 4 , 1 ) and B ( 5 , 1 , 6 ) crosses the xy-plane
  3. The point in x y – plane which is equidistant from the points A ( 1 , – 1 , 0 ) , B ( 2 , 1 , 2 ) and C ( 3 , 2 , – 1 )
  4. The point on z-axis which is equidistant from the points ( 1 , 5 , 7 ) and ( 5 , 1 , – 4 )
  5. The coordinates of a point which is equidistant from the four points O , A , B and C . When O is the origin and A , B , C are the points on the axes of respectively at distances 2,6,4 from the origin in the positive side is
  6. The mid points of the sides of a triangle are ( 1 , 5 , − 1 ) , ( 0 , 4 , − 2 ) , ( 2 , 3 , 4 ) . The distance from origin to the farthest vertex from origin is
  7. The points 2 , 3 , 5 , − 1 , 5 , − 1 , 4 , − 3 , 2 forms
  8. The equation of the line of intersection of planes 4 x + 4 y − 5 z = 12 and 8 x + 12 y − 13 z = 32 can be written as
  9. If A = ( 1 , 2 , 3 ) and B ( 3 , 5 , 7 ) and P , Q are the points on A B such that A P = P Q = Q B , then the mid point of PQ is
  10. If the points ( 5 , 4 , 2 ) , ( 8 , k , − 7 ) and ( 6 , 2 , − 1 ) are collinear, then k =
  11. If the points A , B , C , D are collinear and C , D divide A B in the ratios 2 : 3 , − 2 : 3 respectively, then the ratio in which A divides C D is
  12. The points A ( 2 , 9 , 12 ) , B ( 1 , 8 , 8 ) , C ( − 2 , 11 , 8 ) , D ( − 1 , 12 , 12 ) form
  13. The coordinates of the point which divides lhe line joining the points ( 2 , 3 , 4 ) ind ( 3 , − 4 , 7 ) in the ratio 2 : 4 externally is
  14. If L,M are the feet of the perpendiculars from ( 2 , 4 , 5 ) to x y -plane and yz-plane respectively, then distance LM is
  15. In a three dimensional co-ordinate system P,Q and R are images of a point A(a,b,c) in the xy, yz and zx planes respectively. If G is the centroid of triangle PQR then area of triangle AOG is ( O is the origin )
  16. If A.B.C are projections of P (5,-2,6) on coordinate axes then centriod of △ ABC is
  17. The ortho centre of triangle formed by the points (2,1,5),(3,2,3), (4,0,4) is
  18. If x 1 , y 1 , z 1 , x 2 , y 2 , z 2 and x 3 , y 3 , z 3 are the vertices of an equilateral triangle such that x 1 − 2 2 + y 1 − 3 2 + z 1 − 4 2 = x 2 − 2 2 + y 2 − 3 2 + z 2 − 4 2 = x 3 − 2 2 + y 3 − 3 2 + z 3 − 4 2 then ∑ x 1 + 2 ∑ y 1 + 3 ∑ z 1
  19. If the projections of a line of length d on the coordinate axes are d 1 , d 2 ,   d 3 respectively, then d 1 2 + d 2 2 +   d 3 2 − d 2 =
  20. The projections of a line segment on the axes are 1,2,2. If the length of the segment is n, then log 3 n =
  21. If the projections of the line segment A B ¯ on the coordinate planes are 2 , k , 6 and A B = 6 , then k 2 − 7 =
  22. The projections of the line segment A B ¯ on the axes are 5,12,7. Then the length of A B ¯ is
  23. Let P = 1 , 2 , 0   ,   Q = 4 , 0 , − 2 are any two points in the space. Suppose that d 1 , d 2 are the projections of P Q on the x – axis, y z – p l a n e respectively, then d 1 2 – d 2 2
  24. If α , β are the roots of the quadratic equation x 2 − 5 x + 6 = 0 such that α < β and the vertices of a triangle are A 3 , 5 , − 2 , B α , β , 5 , C − 1 , β , α ,then the triangle is
  25. If the projections of the line segment A B ¯ on the y z – plane, z x – plane, x y – plane are 160 , 153   and   5 respectively, then the projection of A B ¯ on the z – axis is
  26. If ( 2 , 3 , 4 ) is the centroid of the tetrahedron for which ( 2 , 3 , − 1 ) , ( 3 , 0 , − 2 ) , ( − 1 , 4 , 3 ) are three vertices , then the distance of the fourth vertex from the origin is
  27. If A ( 1 , 2 , 3 ) , B ( 2 , 3 , 4 ) and A B is produced up to C such that 2 A B = B C , then C =
  28. The Locus of a point for which the sum of the squares of the distances from the coordinate axes is 16 units is
  29. If Q is the image of P ( – 1 , 2 , – 3 ) with respect to the y z – plane then the distance P Q is
  30. The line passing through the points 5 , 1 , a , 3 , b , 1 crosses the y z – plane at the point 0 , 17 2 , − 13 2 then
  31. The equation of the line passing through the points 0 , 0 , 0 , 3 , 0 , 0 is
  32. The number of octants in which both x – and y – coordinates are negative is
  33. The graph of the equation y 2 + z 2 = 0 in the three – dimensional space is
  34. If P Q be the projections of 3 , − 2 , 4 on the coordinate planes x y , y z respectively then P Q is
  35. If the projections of a line segment of length “ d ” on the coordinate axes are d 1 , d 2 , d 3 respectively then d 1 2 + d 2 2 + d 3 2 =
  36. The coplanar points 3 , 2 , 5 , 2 , 1 , 1 , − 1 , 4 , 1 , 0 , 5 , 5 form a
  37. The points − 1 , 0 , 1 , 0 , 1 , − 1 , 1 , − 1 , 0 , 2 3 , 2 3 , 2 3 form a
  38. The point which divides the line segment joining − 3. − 2 , 4 , − 1 , − 4 , 2 in the ratio 3 : 2 internally is
  39. The line segment joining the points A 2 , 3 , 4 , B − 6 , 5 , − 4 intersect x z – plane at
  40. If the z-coordinate of a point on the line joining the points B 3 , − 2 , 2 and C 6 , − 17 , − 4 is 0 , Then x-coordinate of the point is
  41. Let A and B are two given points. Let P divide A B internally and Q divides A B externally in the same ratio. Then A P , A B , A Q are in
  42. The harmonic conjugate of 2 , 3 , 4 with respect to the points 3 , − 2 , 2 , 6 , − 17 , − 4 is
  43. If A 2 , 3 , − 1 , B 5 , 6 , 3 , C 2 , − 3 , 1 are the vertices of triangle A B C , the length of the median A D is
  44. If D 2 , 1 , 0 , E 2 , 0 , 0 , F 0 , 1 , 0 are mid points of the sides B C , C A , A B of triangle A B C respectively. Then, the centroid of triangle A B C is
  45. Origin is the centroid of the triangle formed by a , 1 , 3 , − 2 , b , − 5 and 4 , 7 , c then ascending order of a , b , c is.
  46. The points P 1 , 3 , 4 , Q − 1 , 6 , 10 , R − 7 , 4 , 7 and S forms Rhombus then S =
  47. If the ortho center and the circum center of a triangle are − 3 , 5 , 2 , 6 , 2 , 5 then its centroid is
  48. The circumcentre of triangle formed by the points 1 , 2 , 3 , 3 , − 1 , 5 , 4 , 0 , − 3 is
  49. The incentre of the triangle formed by 0 , 0 , 0 , 3 , 0 , 0 , 0 , 4 , 0 is
  50. If α , β , γ , are the roots of x 3 − 2 x 2 − 5 x + 6 = 0 , the orthocenter of the triangle with vertices α , β , γ , β , γ , α , γ , α , β is
  51. The distance between the circumcentre and the orthocentre of the triangle formed by 1 , 2 , 3 , 3 , − 1 , 5 , 4 , 0 , − 3 is
  52. If P , Q , R are the images of A 6 , 3 , 2 with respect to the x – , y – , z – axes respectively, then the distance of the centroid of the triangle P Q R from the origin is
  53. The x , y , z coordinates of each vertex of a triangle are in geometric progression .The x and y coordinates of the centroid of the triangle are 1 and 2 respectively. The distance of the centroid from the origin is.
  54. Let A ( 3 , 2 , 0 ) , B ( 5 , 3 , 2 ) , C ( − 9 , 6 , − 3 ) are three points forming a triangle. If A D , the bisector of ∠ B A C meets B C in D , then coordinates of D are
  55. If the point x 1 + t x 2 − x 1 , y 1 + t y 2 − y 1 , z 1 + z 2 − z 1 devides the line segment joining x 1 , y 1 , z 1 ) and x 2 , y 2 , z 2 internally then
  56. A triangle ABC is placed so that the mid-points of the sides are on the x,y,z axes. Lengths of the intercepts made by the plane containing the triangle on these axes are respectively α , β , γ . Coordinates of the centroid of the triangle ABC are
  57. G ( 1 , 1 , − 2 ) is the centroid of the triangle ABC and D is the mid point of BC . If A = ( − 1 , 1 , − 4 ) then D =
  58. α , β , γ are the root of x 3 − 2 x 2 − x + 2 = 0 . Centroid of triangle with verties α , β , γ , ( β , γ , α ) , ( γ , α , β )
  59. If a △ A B C the mid points of the sides A B , B C , C A are respectively ( l , 0 , 0 ) , ( 0 , m , 0 ) and ( 0 , 0 , n ) then A B 2 + B C 2 + C A 2 l 2 + m 2 + n 2 =
  60. In △ A B C if A B = 2 , A C = 20 , B = ( 3 , 2 , 0 ) and C = ( 0 , 1 , 4 ) then the length of the median passing through A is
  61. A ( 5 , 4 , 6 ) , B ( 1 , − 1 , 3 ) and C ( 4 , 3 , 2 ) form △ A B C . If the internal bisector of angle A meets B C in D , then the length of A D ¯ is
  62. The distance between the origin and the centroid of the tetrahedron whose vertices are (0,0,0), (a,0,0), (0,b,0), (0,0,c) is
  63. If ( Cos ⁡ α , sin ⁡ α , 0 ) , ( cos ⁡ β , sin ⁡ β , 0 ) , ( cos ⁡ γ , sin ⁡ γ , 0 ) are vertices of a triangle then circum radius R is
  64. A ( 0 , 2 , 3 ) , B ( 2 , − 1 , 5 ) , C ( 3 , 0 , − 3 ) are vertices of △ A B C . If a , b , c are HG, GS, SH then their increasing order is ( H , G , S are orthocentre, centroid and circumcentre)
  65. A plane is parallel to yz-plane so it is perpendicular to
  66. ln which of the following point lies in a fourth octant? (1 , 2, 3) , (4, -2 ,3) , (4 ,-2 ,-5) and (4 ,2, – 5)
  67. Find the coordinates of a point on Y-axis which are at a distance of 5 2 from the point P(3, – 2,5).
  68. which of the following pairs of points have a distance 43 ?
  69. The equation of the set of points which are equidistant from the points (1,2,3) and (3,2, – 1) is
  70. A point R with x-coordinate 4 lies on the line segment joining the points P(2, – 3, 4) and Q(8, 0, 10). Find the coordinates of the point R
  71. lf there are three points A(2,3, 4), B(- 1,2, – 3) and C(-4,1, – 10) in a space, then they are
  72. A plane is parallel xy-plane, so it is perpendicular to
  73. The locus of a point for which y = 0, z = 0 is
  74. The point ( – 2, – 3, – 4) lies in the
  75. Z is the foot of the perpendicular drawn from a point R(3, 4,5) on the xy -plane. The coordinates of point L are
  76. The distance of point I(3, 4,5) from the yz-plane is
  77. What is the length of foot of perpendicular drawn from the point P (3, 4,5) on Y-axis?
  78. If the distance between the points ( α ,0,1) and (0, 1,2) is 27 , then the value of α is
  79. It A and B be the points (3, 4,5) and (- 1, 3, – 7) respectively, find the equation of the set of points P such that (PA) 2 + (PB) 2 = K 2 , where K is a constant.
  80. Distance of the point (1,2,3) from the coordinate axes are
  81. If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is
  82. The coordinates of a point which is equidistant from the points (0, 0, 0), (o, 0, 0), (0, b, 0), (0,0, c) are given by
  83. If x 2 + y 2 = 1 then the distance from the point x , y , 1 − x 2 − y 2 to the origin is
  84. If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelepiped is
  85. The points A(5, – 1, 1) B(7, – 4,7),C(1, – 6, 10) and D(1 – 3,4) are vertices of a
  86. The points (5, – 4,2),(4,- 3, 1),(7, – 6, 4) and (8, – 7 , 5) are the vertices of
  87. If the coordinates of the vertices of a ∆ ABC are A(- 1, 3, 2), B(2, 3, 5) and C(9, b, – 2), then ∠ A is equal to
  88. Three vertices of a parallelogram ABCD are A(1,2,3), B(- 1, – 2, – 1) and C(2,3,2). Find the fourth vertex D.
  89. Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, – 4,6) in the ratio 2 : 3 externally.
  90. Find the ratio in which the yz-plane divides the line segment formed by joining the points (- 2, 4,7) and (3, – 5, 8).
  91. Find the length of the medians of the triangle with vertices A(0, 0,6),B(0, 4,0) and C(6,0,0).
  92. Find the coordinates of the points which trisect the line segment joining the points P(4,2, – 6) and Q(10, – 16,6).
  93. Find the centroid of a triangle, the mid-point of whose sides are D(1,2, – 3), E(3, 0, 1) and F(- 1,1, – 4).
  94. The mid-points of the sides of a triangle are (5,7 ,11), (0, 8, 5) and (2,3, – 1). Then, the vertices are
  95. The area of the triangle, whose vertices are at the points (2, 1, 1), (3, 1,2) and (- 4,0, 1) is
  96. If vertices of a triangle are A(1,- 1, Z), B(2,0,- 1) and C(0,2,1), then the area of a triangle is
  97. The triangle formed by the points (0,7,10), (- 1,6,6), (- 4,9,6) is
  98. The points (5,2,4),(6,- 1,2) and (8, – 7, k) are collinear, if k is equal to
  99. The point A(1, – 1, 3), B(2, – 4,8) and C(5,- 18, 11) are
  100. The projections of a line segment on x , y and z axes are respectively 3, 4 and 12. The length of the line segment is
  101. A line makes an angle of 60 ° with each of x and y axis, the which it makes with z axis is ( in degrees)
  102. A line A B in three dimensional space makes angles 45 ° and 120 ° with the positive x-axis and positive y-axis respectively. If A B makes an acute angle θ with the positive z-axis, then θ equals ( in degrees)
  103. P (0, 5, 6), Q (1, 4, 7), R (2, 3, 7) and S (3, 4, 6) are four points in the space. The point farthest from the origin O (0, 0, 0) is
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