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← Bihar Board Class 12 PYQ

Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

  1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D2021 Set I2017
    $\vec{k}\times\vec{k}=$
  2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\vec{a} \cdot (\vec{a} \times \vec{a}) =$
  3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set B
    If $\vec{a}=\vec{i}-\vec{j}+2\vec{k}$ and $\vec{b}=2\vec{i}+3\vec{j}-4\vec{k}$ then $|\vec{a}\times\vec{b}| =$
  4. Q4 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set B
    $2\vec{j} \cdot (-3)\vec{k} =$
  5. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D
    If $3\vec{i} + \vec{j} - 2\vec{k}$ and $\vec{i} + \lambda\vec{j} - 3\vec{k}$ are perpendicular to each other…
  6. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set J2026 Set B
    $|\vec{a}|=2,\ |\vec{b}|=3,\ \vec{a}\cdot\vec{b}=4 \Rightarrow |\vec{a}-\vec{b}|=$
  7. Q7 2026 Set A2026 Set C2026 Set F2026 Set J2026 Set B
    $|3\vec{i}+4\vec{j}+7\vec{k}| =$
  8. Q8 2026 Set A2026 Set E2026 Set C2026 Set D2026 Set J2026 Set B
    Find the area of the parallelogram whose adjacent sides are vectors $\vec{i} + 2\vec{j} + 3\vec{k}$ and…
  9. Q9 2026 Set A2026 Set E2026 Set C2026 Set D2026 Set J2026 Set B
    Find the sine of the angle between the two vectors $3\vec{i} + \vec{j} + 2\vec{k}$ and…
  10. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    The projection of the vector $\vec{i}+3\vec{j}+7\vec{k}$ on the vector $2\vec{i}-3\vec{j}+6\vec{k}$ is
  11. Q11 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    If $|\vec{a}+\vec{b}| = |\vec{a}-\vec{b}|$ then
  12. Q12 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D2021 Set I
    $\vec{i}\cdot(\vec{j}\times\vec{k})=$
  13. Q13 2026 Set D
    $|\vec{a}| = 2, |\vec{b}| = 3, \vec{a}\cdot\vec{b} = 4 \Rightarrow |\vec{a}-\vec{b}| =$
  14. Q14 2026 Set D
    If $\vec{a} = \vec{i} - \vec{j} + 2\vec{k}$ and $\vec{b} = 2\vec{i} + 3\vec{j} - 4\vec{k}$ then…
  15. Q15 2026 Set D2026 Set H
    $|3\vec{i} + 4\vec{j} + 7\vec{k}| =$
  16. Q16 2026 Set E
    $2\hat{j} \times (-3)\hat{k} =$
  17. Q17 2026 Set E
    $|\,3\vec{i} + 4\vec{j} + 7\vec{k}\,| =$
  18. Q18 2026 Set F2026 Set H
    Find the area of the parallelogram whose adjacent sides are vectors $\hat{i}+2\hat{j}+3\hat{k}$ and…
  19. Q19 2026 Set F2026 Set H2019 Set F
    Find the sine of the angle between the two vectors $3\hat{i}+\hat{j}+2\hat{k}$ and…
  20. Q20 2026 Set J
    If $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ and $\vec{b}=2\hat{i}+3\hat{j}-4\hat{k}$ then $|\vec{a}\times\vec{b}|=$
  21. Q21 2026 Set J
    $2\hat{j}\cdot(-3)\hat{k}=$
  22. Q22 2025
    If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that…
  23. Q23 2025
    $\hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} =$
  24. Q24 2025
    $|-\hat{i} - \hat{j} - \hat{k}| =$
  25. Q25 2025
    $(2\hat{i}+5\hat{j}-\hat{k})\cdot(-\hat{i}+7\hat{j}+2\hat{k}) =$
  26. Q26 2025
    $\hat{i} \times \hat{k} =$
  27. Q27 2025
    $(\hat{j}+2\hat{k}) \times (\hat{i}+2\hat{j}) =$
  28. Q28 2025
    If $\vec a = 2\hat\imath - \hat\jmath + 2\hat k$ then unit vector $\vec a$ in the direction of vector…
  29. Q29 2025
    If $\vec a = 2\hat\imath+3\hat\jmath+4\hat k,\vec b = -\hat\jmath-2\hat k$ then $|\vec a \times \vec b| =$
  30. Q30 2025
    If $(3\hat\imath-2\hat\jmath+\hat k)$ and $(2\hat\imath-3\hat\jmath-\lambda\hat k)$ are perpendicular to each…
  31. Q31 2025
    $\hat\jmath \cdot (\hat\imath \times \hat k) =$
  32. Q32 2025
    The projection of the vector $\hat\imath - \hat\jmath$ on the vector $\hat\imath + \hat\jmath$ is
  33. Q33 2025
    If $|\vec{a}| = 3, |\vec{b}| = \frac{\sqrt{2}}{3}$ and $\vec{a} \times \vec{b}$ is a unit vector then angle…
  34. Q34 2025
    …
  35. Q35 2025
    $(2\hat{\imath} + 3\hat{\jmath} - 5\hat{k}) \cdot (7\hat{\imath} - \hat{\jmath} + 3\hat{k}) =$
  36. Q36 2025
    If $\vec{a} = \hat{\imath}+\hat{\jmath}+2\hat{k}$ and $\vec{b} = 2\hat{\imath}+\hat{\jmath}+2\hat{k}$ then…
  37. Q37 2025
    Find vector $\vec{v}$ which is perpendicular to $(2\hat{\imath}-\hat{\jmath}+2\hat{k})$ and…
  38. Q38 2025
    If $\vec{a} = \hat{i}-\hat{j}+\hat{k}$ and $\vec{b} = \hat{j}-\hat{k}$ then find $\vec{c}$ such that…
  39. Q39 2025 Set A2025 Set E
    $(4\vec{i} + 3\vec{j})^2 =$
  40. Q40 2025 Set A2024 Set D2024 Set J
    $|\vec{i}-\vec{j}-3\vec{k}| =$
  41. Q41 2025 Set A2025 Set E
    $(7\vec{i} - 8\vec{j} + 9\vec{k}) \cdot (\vec{i} - \vec{j} + \vec{k}) =$
  42. Q42 2025 Set A2025 Set E
    …
  43. Q43 2025 Set A2025 Set E
    $(11\vec{i} + \vec{j} + \vec{k}) \cdot (\vec{i} + \vec{j} + 11\vec{k}) =$
  44. Q44 2025 Set A2025 Set E
    $(\vec{k} \times \vec{j}) \cdot \vec{i} =$
  45. Q45 2025 Set A2025 Set E
    $(\vec{i} - 2\vec{j} + 5\vec{k}) \cdot (-2\vec{i} + 4\vec{j} + 2\vec{k}) =$
  46. Q46 2025 Set A2025 Set E
    $(i \times j) + (\vec{i} \times \vec{i}) =$
  47. Q47 2025 Set E
    $|\vec{i} - \vec{j} - 3\vec{k}| =$
  48. Q48 2025 Set E
    Find the value of $x$, when the following vectors are perpendicular to one another…
  49. Q49 2024 Set D2024 Set J2018
    If $\vec{a} = \vec{i} + \vec{j} + 2\vec{k}$, then the corresponding unit vector $\hat{a}$ in the direction of…
  50. Q50 2024 Set D2024 Set J
    $(\vec{i}+3\vec{j}-2\vec{k})\times(-\vec{i}+3\vec{k})=$
  51. Q51 2024 Set D
    The angle between the vectors $2\vec{i} - 3\vec{j} + 2\vec{k}$ and $\vec{i} + 4\vec{j} + 5\vec{k}$ is
  52. Q52 2024 Set D2024 Set J
    $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| \Rightarrow$
  53. Q53 2024 Set D2024 Set J
    The projection of the vector $\vec{i} - 2\vec{j} + \vec{k}$ on the vector $4\vec{i} - 4\vec{j} + 7\vec{k}$ is
  54. Q54 2024 Set D
    If $\vec{a} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}$ then find the value…
  55. Q55 2024 Set D
    Evaluate: $(\vec i-3\vec j+4\vec k)\cdot[(2\vec i-\vec j)\times(\vec j+\vec k)]$.
  56. Q56 2024 Set D2024 Set J20162015
    $\vec{k}\cdot\vec{j}=$
  57. Q57 2024 Set D2024 Set J
    $(4\vec{i}+3\vec{j}+3\vec{k})\cdot(6\vec{i}-4\vec{j}+\vec{k})=$
  58. Q58 2024 Set D2024 Set J
    $\vec{a}\times(\vec{b}+\vec{c})+\vec{b}\times(\vec{c}+\vec{a})+\vec{c}\times(\vec{a}+\vec{b}) =$
  59. Q59 2024 Set J2018
    The direction cosines of the vector $3\vec{i} - 4\vec{j} + 12\vec{k}$ is
  60. Q60 2024 Set J
    The angle between the vectors $2\vec{i}-3\vec{j}+2\vec{k}$ and $\vec{i}+4\vec{j}+5\vec{k}$ is
  61. Q61 2024 Set J
    If $\vec{a} = \vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = 2\vec{i} + \vec{j} + 3\vec{k}$ then find the value…
  62. Q62 2024 Set J
    Evaluate : $(\vec i-3\vec j+4\vec k)\cdot\left[(2\vec i-\vec j)\times(\vec j+\vec k)\right]$.
  63. Q63 20232023 Set E2017
    $\vec{j} \times \vec{k} =$
  64. Q64 2023
    $|3\vec{i}-4\vec{j}-5\vec{k}|$
  65. Q65 2023
    $(\vec{j} - 2\vec{i}) \cdot (\vec{k} + 3\vec{i} - \vec{j}) =$
  66. Q66 2023
    $(2\vec{i} - 3\vec{j}).(\vec{i} + \vec{k}) =$
  67. Q67 2023
    $\vec{i}.\vec{i} =$
  68. Q68 20232023 Set E
    $3\vec{k} \cdot (13\vec{i} - 7\vec{k}) =$
  69. Q69 2023
    $\left(3\vec{i} - 4\vec{k}\right)^2 =$
  70. Q70 20232023 Set E
    The unit vector in the direction of vector $3\vec{i} - 9\vec{j}$ is
  71. Q71 20232023 Set E
    $(\vec{i} - \vec{j} + \vec{k}) \cdot (7\vec{i} - 8\vec{j} + 9\vec{k}) =$
  72. Q72 20232023 Set E
    $(11\vec{i} - 7\vec{j} - \vec{k}) \cdot (8\vec{i} - \vec{j} - 5\vec{k}) =$
  73. Q73 2023
    $(3\vec{k}-7\vec{i})\times 2\vec{k}=$
  74. Q74 20232023 Set E
    $|\vec{i}-2\vec{j}+2\vec{k}|=$
  75. Q75 20232023 Set E
    $(10\vec{i}+\vec{j}+\vec{k}) \times (-4\vec{i}+7\vec{j}-11\vec{k}) =$
  76. Q76 2023
    $\vec{k}.(\vec{i}+\vec{j}) =$
  77. Q77 2023 Set E
    $(\vec{j}-2\vec{i})\cdot(\vec{k}+3\vec{i}-\vec{j}) =$
  78. Q78 2023 Set E
    $(2\vec{i}-3\vec{j})\cdot(\vec{i}+\vec{k})=$
  79. Q79 2023 Set E
    $\vec{k}\cdot(\vec{i}+\vec{j}) =$
  80. Q80 2023 Set E
    $(3\vec k-7\vec i)\times2\vec k=$
  81. Q81 2023 Set E
    $(3\vec{i} - 4\vec{k})^2 =$
  82. Q82 2023 Set E
    $|3\vec{i} - 4\vec{j} - 5\vec{k}| =$
  83. Q83 2023 Set E2015
    $\vec{i}\cdot\vec{j}=$
  84. Q84 2021 Set I
    $[\vec{a}\ \vec{a}\ \vec{a}] =$
  85. Q85 2021 Set J2021 Set I
    The modulus of $x\vec{i}+y\vec{j}+z\vec{k}$ is
  86. Q86 2021 Set J2021 Set I
    The number of unit vector(s) perpendicular to a plane is
  87. Q87 2021 Set J2021 Set I
    If $\vec a=2\hat i-\hat j+2\hat k$ and $\vec b=-\hat i+\hat j-\hat k$, then
  88. Q88 2021 Set J2021 Set I
    $\hat{n}^2 =$
  89. Q89 2021 Set J2021 Set I2015
    $\vec{a}\cdot\vec{a}=$
  90. Q90 2021 Set J2021 Set I
    $\vec{j}\cdot(\vec{k}\times\vec{i}) =$
  91. Q91 2021 Set J2021 Set I
    $[\vec{x}\ \vec{y}\ \vec{z}] =$
  92. Q92 2021 Set J2021 Set I
    $\vec{k}\times(\vec{i}\times\vec{j}) =$
  93. Q93 2021 Set J
    $|\vec a\ \vec a\ \vec a|=$
  94. Q94 2021 Set J
    $\hat i\times\hat k=$
  95. Q95 2021 Set J
    $\vec a\times\vec b=$
  96. Q96 2021 Set J2021 Set I
    If $\vec{a} \perp \vec{b}$, then $\vec{a} \cdot \vec{b} =$
  97. Q97 2021 Set J
    $\hat{i} \cdot (\hat{j} \times \hat{k}) =$
  98. Q98 2019 Set F
    $\vec{a}\cdot\vec{b} = ?$
  99. Q99 2019 Set F
    The modulus of the vector $19\hat{i}+5\hat{j}-6\hat{k}$ is -
  100. Q100 2019 Set F
    $\vec{k} \times \vec{k} = ?$
  101. Q101 2019 Set F
    If $\vec a = \hat i + \hat j + 2\hat k$ and $\vec b = 3\hat i + 2\hat j - \hat k$, then the value of…
  102. Q102 2019 Set F
    $(\vec a \times \vec a)\cdot\vec b = ?$
  103. Q103 2019 Set F20162015
    If $\vec{a}=2\hat{i}-3\hat{j}-5\hat{k}$ and $\vec{b}=-7\hat{i}+6\hat{j}+8\hat{k}$, find $\vec{a}\times\vec{b}$
  104. Q104 2019 Set F2016
    The position vector of the point $(x, y, z)$ is
  105. Q105 2018
    $x\vec{i} - 3\vec{j} + 5\vec{k},\ -x\vec{i} + x\vec{j} + 2\vec{k}$ are perpendicular to each other then value…
  106. Q106 2018
    …
  107. Q107 2018
    Find the value of P, if: $(2\vec i+6\vec j+27\vec k)\times(\vec i+3\vec j+p\vec k)=\vec 0$
  108. Q108 2017
    The position vector of the point $(4,5,6)$ is
  109. Q109 2017
    If $\overrightarrow{OA} = 2\vec{i} + 5\vec{j} - 2\vec{k}$ and…
  110. Q110 2017
    If $\vec{a} = \vec{i} + \vec{j} + 3\vec{k}; \vec{b} = 2\vec{i} + 3\vec{j} - 5\vec{k}$ then $\vec{a}.\vec{b} =$
  111. Q111 2017
    If $\vec{a}$ and $\vec{b}$ are mutually perpendicular then $3\vec{j}$
  112. Q112 2017
    If $\vec{a} = \hat{i} - 2\hat{j} - 3\hat{k}$; $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ and…
  113. Q113 2016
    $\left|-\vec{i}+2\vec{j}-3\vec{k}\right|=$
  114. Q114 2016
    If the position vectors of the points A and B be respectively (1, 2, 3) and (-3, -4, 0) then…
  115. Q115 2016
    If $\vec{a}=3\vec{i}+2\vec{j}+\vec{k}, \vec{b}=4\vec{i}-5\vec{j}+3\vec{k}$, then $\vec{a}\cdot\vec{b}$
  116. Q116 2016
    If $\vec{a}$ and $\vec{b}$ are perpendicular to each other then
  117. Q117 2016
    $\vec{i}\times\vec{j}=$
  118. Q118 2015
    The positive vector of the point $(1, 0, 2)$ is
  119. Q119 2015
    The modulus of $7\vec{i} - 2\vec{j} + \vec{k}$
  120. Q120 2015
    If O be the origin and $\overrightarrow{OP} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ and…
  121. Q121 2015
    The scalar product of $5\hat{i} + \hat{j} - 3\hat{k}$ and $3\hat{i} - 4\hat{j} + 7\hat{k}$ is
  122. Q122 2015
    If $\vec{a}\cdot\vec{b}=0$ then