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Chapter 10: Vector Algebra

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

100

Questions

0

Topics

Solved Questions

Q1. If a⃗ = 2i + 3j + k, then |a⃗| is:

√14
√6
6
14

Difficulty: Easy · Topic: Magnitude

Solution

|a⃗| = √(4+9+1) = √14.

Q2. The cross product of i × j is:

0
k
-k
i+j

Difficulty: Easy · Topic: Cross Product

Solution

i × j = k (right-hand rule). j × i = -k.

Q3. |1i+0j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+0²)=1.0.

Q4. |1i+0j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+1²)=1.41.

Q5. |1i+0j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+2²)=2.24.

Q6. |1i+0j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+3²)=3.16.

Q7. |1i+0j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+4²)=4.12.

Q8. |1i+0j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+5²)=5.1.

Q9. |1i+0j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+6²)=6.08.

Q10. |1i+0j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+7²)=7.07.

Q11. |1i+0j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+8²)=8.06.

Q12. |1i+0j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+0²+9²)=9.06.

Q13. |1i+1j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+0²)=1.41.

Q14. |1i+1j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+1²)=1.73.

Q15. |1i+1j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+2²)=2.45.

Q16. |1i+1j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+3²)=3.32.

Q17. |1i+1j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+4²)=4.24.

Q18. |1i+1j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+5²)=5.2.

Q19. |1i+1j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+6²)=6.16.

Q20. |1i+1j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+7²)=7.14.

Q21. |1i+1j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+8²)=8.12.

Q22. |1i+1j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+1²+9²)=9.11.

Q23. |1i+2j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+0²)=2.24.

Q24. |1i+2j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+1²)=2.45.

Q25. |1i+2j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+2²)=3.0.

Q26. |1i+2j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+3²)=3.74.

Q27. |1i+2j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+4²)=4.58.

Q28. |1i+2j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+5²)=5.48.

Q29. |1i+2j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+6²)=6.4.

Q30. |1i+2j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+7²)=7.35.

Q31. |1i+2j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+8²)=8.31.

Q32. |1i+2j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+2²+9²)=9.27.

Q33. |1i+3j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+0²)=3.16.

Q34. |1i+3j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+1²)=3.32.

Q35. |1i+3j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+2²)=3.74.

Q36. |1i+3j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+3²)=4.36.

Q37. |1i+3j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+4²)=5.1.

Q38. |1i+3j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+5²)=5.92.

Q39. |1i+3j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+6²)=6.78.

Q40. |1i+3j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+7²)=7.68.

Q41. |1i+3j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+8²)=8.6.

Q42. |1i+3j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+3²+9²)=9.54.

Q43. |1i+4j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+0²)=4.12.

Q44. |1i+4j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+1²)=4.24.

Q45. |1i+4j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+2²)=4.58.

Q46. |1i+4j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+3²)=5.1.

Q47. |1i+4j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+4²)=5.74.

Q48. |1i+4j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+5²)=6.48.

Q49. |1i+4j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+6²)=7.28.

Q50. |1i+4j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+7²)=8.12.

Q51. |1i+4j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+8²)=9.0.

Q52. |1i+4j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+4²+9²)=9.9.

Q53. |1i+5j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+0²)=5.1.

Q54. |1i+5j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+1²)=5.2.

Q55. |1i+5j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+2²)=5.48.

Q56. |1i+5j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+3²)=5.92.

Q57. |1i+5j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+4²)=6.48.

Q58. |1i+5j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+5²)=7.14.

Q59. |1i+5j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+6²)=7.87.

Q60. |1i+5j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+7²)=8.66.

Q61. |1i+5j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+8²)=9.49.

Q62. |1i+5j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+5²+9²)=10.34.

Q63. |1i+6j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+0²)=6.08.

Q64. |1i+6j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+1²)=6.16.

Q65. |1i+6j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+2²)=6.4.

Q66. |1i+6j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+3²)=6.78.

Q67. |1i+6j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+4²)=7.28.

Q68. |1i+6j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+5²)=7.87.

Q69. |1i+6j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+6²)=8.54.

Q70. |1i+6j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+7²)=9.27.

Q71. |1i+6j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+8²)=10.05.

Q72. |1i+6j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+6²+9²)=10.86.

Q73. |1i+7j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+0²)=7.07.

Q74. |1i+7j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+1²)=7.14.

Q75. |1i+7j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+2²)=7.35.

Q76. |1i+7j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+3²)=7.68.

Q77. |1i+7j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+4²)=8.12.

Q78. |1i+7j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+5²)=8.66.

Q79. |1i+7j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+6²)=9.27.

Q80. |1i+7j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+7²)=9.95.

Q81. |1i+7j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+8²)=10.68.

Q82. |1i+7j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+7²+9²)=11.45.

Q83. |1i+8j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+0²)=8.06.

Q84. |1i+8j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+1²)=8.12.

Q85. |1i+8j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+2²)=8.31.

Q86. |1i+8j+3k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+3²)=8.6.

Q87. |1i+8j+4k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+4²)=9.0.

Q88. |1i+8j+5k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+5²)=9.49.

Q89. |1i+8j+6k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+6²)=10.05.

Q90. |1i+8j+7k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+7²)=10.68.

Q91. |1i+8j+8k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+8²)=11.36.

Q92. |1i+8j+9k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+8²+9²)=12.08.

Q93. |1i+9j+0k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+9²+0²)=9.06.

Q94. |1i+9j+1k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+9²+1²)=9.11.

Q95. |1i+9j+2k| =

Difficulty: Easy · Topic: Vectors

Solution

√(1²+9²+2²)=9.27.

Q96. The angle between vectors a⃗ = i+j and b⃗ = j+k is:

60°
90°
45°
30°

Difficulty: Easy-Medium · Topic: Angle Between Vectors

Solution

a⃗·b⃗ = 0+1+0 = 1. |a⃗|=√2, |b⃗|=√2. cosθ = 1/2. θ = 60°.

Q97. a⃗ × b⃗ = -b⃗ × a⃗ shows cross product is:

distributive
anti-commutative
commutative
associative

Difficulty: Easy-Medium · Topic: Vector Algebra

Solution

anti-commutative.

Q98. a⃗ · b⃗ = |a||b|cosθ is the:

scalar triple product
cross product
dot product
triple product

Difficulty: Easy-Medium · Topic: Vector Algebra

Solution

dot product.

Q99. |a⃗ × b⃗| = |a||b|sinθ gives:

volume of parallelepiped
length of diagonal
perimeter
area of parallelogram

Difficulty: Easy-Medium · Topic: Vector Algebra

Solution

area of parallelogram.

Q100. [a⃗ b⃗ c⃗] gives the:

perimeter
area of triangle
volume of parallelepiped
length

Difficulty: Easy-Medium · Topic: Vector Algebra

Solution

volume of parallelepiped.

Other Chapters in Mathematics

Ch 1: Relations & Functions Ch 2: Inverse Trig Functions Ch 3: Matrices Ch 4: Determinants Ch 5: Continuity & Differentiability Ch 6: Applications of Derivatives Ch 7: Integrals Ch 8: Applications of Integrals Ch 9: Differential Equations Ch 11: Three Dimensional Geometry Ch 12: Linear Programming Ch 13: Probability

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