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NCERT Solutions › Mathematics › Chapter 11

Chapter 11: Three Dimensional Geometry

NCERT Solutions for CBSE Class 10 Mathematics — 100 solved questions with detailed explanations.

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Solved Questions

Q1. Distance between (0,0,0) and (1,3,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(3-0)²+(2-0)²)=3.74.

Q2. Distance between (0,0,0) and (2,3,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(3-0)²+(2-0)²)=4.12.

Q3. Distance between (0,0,0) and (3,3,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(3-0)²+(2-0)²)=4.69.

Q4. Distance between (0,0,0) and (4,3,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(3-0)²+(2-0)²)=5.39.

Q5. Distance between (0,0,0) and (5,3,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(3-0)²+(2-0)²)=6.16.

Q6. Distance between (0,0,0) and (6,3,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(3-0)²+(2-0)²)=7.0.

Q7. Distance between (0,0,1) and (1,3,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(3-0)²+(3-1)²)=3.74.

Q8. Distance between (0,0,1) and (2,3,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(3-0)²+(3-1)²)=4.12.

Q9. Distance between (0,0,1) and (3,3,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(3-0)²+(3-1)²)=4.69.

Q10. Distance between (0,0,1) and (4,3,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(3-0)²+(3-1)²)=5.39.

Q11. Distance between (0,0,1) and (5,3,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(3-0)²+(3-1)²)=6.16.

Q12. Distance between (0,0,1) and (6,3,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(3-0)²+(3-1)²)=7.0.

Q13. Distance between (0,0,2) and (1,3,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(3-0)²+(4-2)²)=3.74.

Q14. Distance between (0,0,2) and (2,3,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(3-0)²+(4-2)²)=4.12.

Q15. Distance between (0,0,2) and (3,3,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(3-0)²+(4-2)²)=4.69.

Q16. Distance between (0,0,2) and (4,3,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(3-0)²+(4-2)²)=5.39.

Q17. Distance between (0,0,2) and (5,3,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(3-0)²+(4-2)²)=6.16.

Q18. Distance between (0,0,2) and (6,3,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(3-0)²+(4-2)²)=7.0.

Q19. Distance between (0,0,3) and (1,3,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(3-0)²+(0-3)²)=4.36.

Q20. Distance between (0,0,3) and (2,3,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(3-0)²+(0-3)²)=4.69.

Q21. Distance between (0,0,3) and (3,3,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(3-0)²+(0-3)²)=5.2.

Q22. Distance between (0,0,3) and (4,3,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(3-0)²+(0-3)²)=5.83.

Q23. Distance between (0,0,3) and (5,3,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(3-0)²+(0-3)²)=6.56.

Q24. Distance between (0,0,3) and (6,3,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(3-0)²+(0-3)²)=7.35.

Q25. Distance between (0,1,0) and (1,4,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(4-1)²+(2-0)²)=3.74.

Q26. Distance between (0,1,0) and (2,4,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(4-1)²+(2-0)²)=4.12.

Q27. Distance between (0,1,0) and (3,4,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(4-1)²+(2-0)²)=4.69.

Q28. Distance between (0,1,0) and (4,4,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(4-1)²+(2-0)²)=5.39.

Q29. Distance between (0,1,0) and (5,4,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(4-1)²+(2-0)²)=6.16.

Q30. Distance between (0,1,0) and (6,4,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(4-1)²+(2-0)²)=7.0.

Q31. Distance between (0,1,1) and (1,4,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(4-1)²+(3-1)²)=3.74.

Q32. Distance between (0,1,1) and (2,4,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(4-1)²+(3-1)²)=4.12.

Q33. Distance between (0,1,1) and (3,4,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(4-1)²+(3-1)²)=4.69.

Q34. Distance between (0,1,1) and (4,4,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(4-1)²+(3-1)²)=5.39.

Q35. Distance between (0,1,1) and (5,4,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(4-1)²+(3-1)²)=6.16.

Q36. Distance between (0,1,1) and (6,4,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(4-1)²+(3-1)²)=7.0.

Q37. Distance between (0,1,2) and (1,4,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(4-1)²+(4-2)²)=3.74.

Q38. Distance between (0,1,2) and (2,4,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(4-1)²+(4-2)²)=4.12.

Q39. Distance between (0,1,2) and (3,4,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(4-1)²+(4-2)²)=4.69.

Q40. Distance between (0,1,2) and (4,4,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(4-1)²+(4-2)²)=5.39.

Q41. Distance between (0,1,2) and (5,4,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(4-1)²+(4-2)²)=6.16.

Q42. Distance between (0,1,2) and (6,4,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(4-1)²+(4-2)²)=7.0.

Q43. Distance between (0,1,3) and (1,4,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(4-1)²+(0-3)²)=4.36.

Q44. Distance between (0,1,3) and (2,4,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(4-1)²+(0-3)²)=4.69.

Q45. Distance between (0,1,3) and (3,4,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(4-1)²+(0-3)²)=5.2.

Q46. Distance between (0,1,3) and (4,4,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(4-1)²+(0-3)²)=5.83.

Q47. Distance between (0,1,3) and (5,4,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(4-1)²+(0-3)²)=6.56.

Q48. Distance between (0,1,3) and (6,4,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(4-1)²+(0-3)²)=7.35.

Q49. Distance between (0,2,0) and (1,5,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(5-2)²+(2-0)²)=3.74.

Q50. Distance between (0,2,0) and (2,5,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(5-2)²+(2-0)²)=4.12.

Q51. Distance between (0,2,0) and (3,5,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(5-2)²+(2-0)²)=4.69.

Q52. Distance between (0,2,0) and (4,5,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(5-2)²+(2-0)²)=5.39.

Q53. Distance between (0,2,0) and (5,5,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(5-2)²+(2-0)²)=6.16.

Q54. Distance between (0,2,0) and (6,5,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(5-2)²+(2-0)²)=7.0.

Q55. Distance between (0,2,1) and (1,5,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(5-2)²+(3-1)²)=3.74.

Q56. Distance between (0,2,1) and (2,5,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(5-2)²+(3-1)²)=4.12.

Q57. Distance between (0,2,1) and (3,5,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(5-2)²+(3-1)²)=4.69.

Q58. Distance between (0,2,1) and (4,5,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(5-2)²+(3-1)²)=5.39.

Q59. Distance between (0,2,1) and (5,5,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(5-2)²+(3-1)²)=6.16.

Q60. Distance between (0,2,1) and (6,5,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(5-2)²+(3-1)²)=7.0.

Q61. Distance between (0,2,2) and (1,5,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(5-2)²+(4-2)²)=3.74.

Q62. Distance between (0,2,2) and (2,5,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(5-2)²+(4-2)²)=4.12.

Q63. Distance between (0,2,2) and (3,5,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(5-2)²+(4-2)²)=4.69.

Q64. Distance between (0,2,2) and (4,5,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(5-2)²+(4-2)²)=5.39.

Q65. Distance between (0,2,2) and (5,5,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(5-2)²+(4-2)²)=6.16.

Q66. Distance between (0,2,2) and (6,5,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(5-2)²+(4-2)²)=7.0.

Q67. Distance between (0,2,3) and (1,5,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(5-2)²+(0-3)²)=4.36.

Q68. Distance between (0,2,3) and (2,5,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(5-2)²+(0-3)²)=4.69.

Q69. Distance between (0,2,3) and (3,5,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(5-2)²+(0-3)²)=5.2.

Q70. Distance between (0,2,3) and (4,5,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(5-2)²+(0-3)²)=5.83.

Q71. Distance between (0,2,3) and (5,5,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(5-2)²+(0-3)²)=6.56.

Q72. Distance between (0,2,3) and (6,5,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(5-2)²+(0-3)²)=7.35.

Q73. Distance between (0,3,0) and (1,6,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(6-3)²+(2-0)²)=3.74.

Q74. Distance between (0,3,0) and (2,6,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(6-3)²+(2-0)²)=4.12.

Q75. Distance between (0,3,0) and (3,6,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(6-3)²+(2-0)²)=4.69.

Q76. Distance between (0,3,0) and (4,6,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(6-3)²+(2-0)²)=5.39.

Q77. Distance between (0,3,0) and (5,6,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(6-3)²+(2-0)²)=6.16.

Q78. Distance between (0,3,0) and (6,6,2):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(6-3)²+(2-0)²)=7.0.

Q79. Distance between (0,3,1) and (1,6,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(6-3)²+(3-1)²)=3.74.

Q80. Distance between (0,3,1) and (2,6,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(6-3)²+(3-1)²)=4.12.

Q81. Distance between (0,3,1) and (3,6,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(6-3)²+(3-1)²)=4.69.

Q82. Distance between (0,3,1) and (4,6,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(6-3)²+(3-1)²)=5.39.

Q83. Distance between (0,3,1) and (5,6,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(6-3)²+(3-1)²)=6.16.

Q84. Distance between (0,3,1) and (6,6,3):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(6-3)²+(3-1)²)=7.0.

Q85. Distance between (0,3,2) and (1,6,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(6-3)²+(4-2)²)=3.74.

Q86. Distance between (0,3,2) and (2,6,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(6-3)²+(4-2)²)=4.12.

Q87. Distance between (0,3,2) and (3,6,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(6-3)²+(4-2)²)=4.69.

Q88. Distance between (0,3,2) and (4,6,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(6-3)²+(4-2)²)=5.39.

Q89. Distance between (0,3,2) and (5,6,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(6-3)²+(4-2)²)=6.16.

Q90. Distance between (0,3,2) and (6,6,4):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((6-0)²+(6-3)²+(4-2)²)=7.0.

Q91. Distance between (0,3,3) and (1,6,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((1-0)²+(6-3)²+(0-3)²)=4.36.

Q92. Distance between (0,3,3) and (2,6,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((2-0)²+(6-3)²+(0-3)²)=4.69.

Q93. Distance between (0,3,3) and (3,6,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((3-0)²+(6-3)²+(0-3)²)=5.2.

Q94. Distance between (0,3,3) and (4,6,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((4-0)²+(6-3)²+(0-3)²)=5.83.

Q95. Distance between (0,3,3) and (5,6,0):

Difficulty: Easy · Topic: 3D Distance

Solution

d=√((5-0)²+(6-3)²+(0-3)²)=6.56.

Q96. The direction cosines of a line making equal angles with all three axes are:

Difficulty: Easy-Medium · Topic: Direction Cosines

Solution

If α=β=γ, then l=m=n. l²+m²+n²=1 ⇒ 3l²=1 ⇒ l=m=n=1/√3.

Q97. The distance of point (1,2,3) from the plane x+2y+2z=13 is:

Difficulty: Easy-Medium · Topic: Distance from Plane

Solution

d = |1+4+6-13|/√(1+4+4) = |-2|/3 = 2/3. Wait: |1+2(2)+2(3)-13|/√(1+4+4) = |1+4+6-13|/3 = 2/3.

Q98. Direction ratios of x-axis are:

Difficulty: Easy-Medium · Topic: Three Dimensional Geometry

Solution

(1,0,0).

Q99. Angle between two planes is angle between their:

Difficulty: Easy-Medium · Topic: Three Dimensional Geometry

Solution

normal vectors.

Q100. Equation of plane through (a,b,c) with normal (l,m,n) is:

Difficulty: Easy-Medium · Topic: Three Dimensional Geometry

Solution

l(x-a)+m(y-b)+n(z-c)=0.

Other Chapters in Mathematics

Ch 1: Relations & FunctionsCh 2: Inverse Trig FunctionsCh 3: MatricesCh 4: DeterminantsCh 5: Continuity & DifferentiabilityCh 6: Applications of DerivativesCh 7: IntegralsCh 8: Applications of IntegralsCh 9: Differential EquationsCh 10: Vector AlgebraCh 12: Linear ProgrammingCh 13: Probability

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