Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

86 of 122 · show all

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

   $\vec{k}\times\vec{k}=$

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2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\vec{a} \cdot (\vec{a} \times \vec{a}) =$

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3. Q4 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set B

   $2\vec{j} \cdot (-3)\vec{k} =$

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4. 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…

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5. Q7 2026 Set A2026 Set C2026 Set F2026 Set J2026 Set B

   $|3\vec{i}+4\vec{j}+7\vec{k}| =$

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6. 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

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7. Q12 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D2021 Set I

   $\vec{i}\cdot(\vec{j}\times\vec{k})=$

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8. Q15 2026 Set D2026 Set H

   $|3\vec{i} + 4\vec{j} + 7\vec{k}| =$

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9. Q16 2026 Set E

   $2\hat{j} \times (-3)\hat{k} =$

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10. Q17 2026 Set E

    $|\,3\vec{i} + 4\vec{j} + 7\vec{k}\,| =$

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11. Q21 2026 Set J

    $2\hat{j}\cdot(-3)\hat{k}=$

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12. Q23 2025

    $\hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} =$

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13. Q24 2025

    $|-\hat{i} - \hat{j} - \hat{k}| =$

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14. Q25 2025

    $(2\hat{i}+5\hat{j}-\hat{k})\cdot(-\hat{i}+7\hat{j}+2\hat{k}) =$

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15. Q26 2025

    $\hat{i} \times \hat{k} =$

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16. Q28 2025

    If $\vec a = 2\hat\imath - \hat\jmath + 2\hat k$ then unit vector $\vec a$ in the direction of vector…

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17. 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…

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18. Q31 2025

    $\hat\jmath \cdot (\hat\imath \times \hat k) =$

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19. Q32 2025

    The projection of the vector $\hat\imath - \hat\jmath$ on the vector $\hat\imath + \hat\jmath$ is

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20. Q34 2025

    …

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21. Q35 2025

    $(2\hat{\imath} + 3\hat{\jmath} - 5\hat{k}) \cdot (7\hat{\imath} - \hat{\jmath} + 3\hat{k}) =$

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22. Q39 2025 Set A2025 Set E

    $(4\vec{i} + 3\vec{j})^2 =$

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23. Q40 2025 Set A2024 Set D2024 Set J

    $|\vec{i}-\vec{j}-3\vec{k}| =$

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24. Q41 2025 Set A2025 Set E

    $(7\vec{i} - 8\vec{j} + 9\vec{k}) \cdot (\vec{i} - \vec{j} + \vec{k}) =$

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25. Q42 2025 Set A2025 Set E

    …

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26. Q43 2025 Set A2025 Set E

    $(11\vec{i} + \vec{j} + \vec{k}) \cdot (\vec{i} + \vec{j} + 11\vec{k}) =$

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27. Q44 2025 Set A2025 Set E

    $(\vec{k} \times \vec{j}) \cdot \vec{i} =$

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28. Q45 2025 Set A2025 Set E

    $(\vec{i} - 2\vec{j} + 5\vec{k}) \cdot (-2\vec{i} + 4\vec{j} + 2\vec{k}) =$

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29. Q46 2025 Set A2025 Set E

    $(i \times j) + (\vec{i} \times \vec{i}) =$

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30. Q47 2025 Set E

    $|\vec{i} - \vec{j} - 3\vec{k}| =$

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31. 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…

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32. Q52 2024 Set D2024 Set J

    $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| \Rightarrow$

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33. 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…

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34. Q56 2024 Set D2024 Set J20162015

    $\vec{k}\cdot\vec{j}=$

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35. Q57 2024 Set D2024 Set J

    $(4\vec{i}+3\vec{j}+3\vec{k})\cdot(6\vec{i}-4\vec{j}+\vec{k})=$

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36. Q59 2024 Set J2018

    The direction cosines of the vector $3\vec{i} - 4\vec{j} + 12\vec{k}$ is

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37. 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…

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38. Q63 20232023 Set E2017

    $\vec{j} \times \vec{k} =$

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39. Q64 2023

    $|3\vec{i}-4\vec{j}-5\vec{k}|$

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40. Q66 2023

    $(2\vec{i} - 3\vec{j}).(\vec{i} + \vec{k}) =$

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41. Q67 2023

    $\vec{i}.\vec{i} =$

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42. Q68 20232023 Set E

    $3\vec{k} \cdot (13\vec{i} - 7\vec{k}) =$

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43. Q69 2023

    $\left(3\vec{i} - 4\vec{k}\right)^2 =$

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44. Q70 20232023 Set E

    The unit vector in the direction of vector $3\vec{i} - 9\vec{j}$ is

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45. Q71 20232023 Set E

    $(\vec{i} - \vec{j} + \vec{k}) \cdot (7\vec{i} - 8\vec{j} + 9\vec{k}) =$

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46. Q72 20232023 Set E

    $(11\vec{i} - 7\vec{j} - \vec{k}) \cdot (8\vec{i} - \vec{j} - 5\vec{k}) =$

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47. Q74 20232023 Set E

    $|\vec{i}-2\vec{j}+2\vec{k}|=$

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48. Q76 2023

    $\vec{k}.(\vec{i}+\vec{j}) =$

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49. Q77 2023 Set E

    $(\vec{j}-2\vec{i})\cdot(\vec{k}+3\vec{i}-\vec{j}) =$

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50. Q78 2023 Set E

    $(2\vec{i}-3\vec{j})\cdot(\vec{i}+\vec{k})=$

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51. Q79 2023 Set E

    $\vec{k}\cdot(\vec{i}+\vec{j}) =$

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52. Q81 2023 Set E

    $(3\vec{i} - 4\vec{k})^2 =$

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53. Q82 2023 Set E

    $|3\vec{i} - 4\vec{j} - 5\vec{k}| =$

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54. Q83 2023 Set E2015

    $\vec{i}\cdot\vec{j}=$

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55. Q84 2021 Set I

    $[\vec{a}\ \vec{a}\ \vec{a}] =$

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56. Q85 2021 Set J2021 Set I

    The modulus of $x\vec{i}+y\vec{j}+z\vec{k}$ is

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57. Q86 2021 Set J2021 Set I

    The number of unit vector(s) perpendicular to a plane is

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58. Q88 2021 Set J2021 Set I

    $\hat{n}^2 =$

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59. Q89 2021 Set J2021 Set I2015

    $\vec{a}\cdot\vec{a}=$

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60. Q90 2021 Set J2021 Set I

    $\vec{j}\cdot(\vec{k}\times\vec{i}) =$

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61. Q91 2021 Set J2021 Set I

    $[\vec{x}\ \vec{y}\ \vec{z}] =$

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62. Q92 2021 Set J2021 Set I

    $\vec{k}\times(\vec{i}\times\vec{j}) =$

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63. Q93 2021 Set J

    $|\vec a\ \vec a\ \vec a|=$

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64. Q94 2021 Set J

    $\hat i\times\hat k=$

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65. Q95 2021 Set J

    $\vec a\times\vec b=$

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66. Q96 2021 Set J2021 Set I

    If $\vec{a} \perp \vec{b}$, then $\vec{a} \cdot \vec{b} =$

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67. Q97 2021 Set J

    $\hat{i} \cdot (\hat{j} \times \hat{k}) =$

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68. Q98 2019 Set F

    $\vec{a}\cdot\vec{b} = ?$

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69. Q99 2019 Set F

    The modulus of the vector $19\hat{i}+5\hat{j}-6\hat{k}$ is -

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70. Q100 2019 Set F

    $\vec{k} \times \vec{k} = ?$

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71. Q102 2019 Set F

    $(\vec a \times \vec a)\cdot\vec b = ?$

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72. Q104 2019 Set F2016

    The position vector of the point $(x, y, z)$ is

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73. Q108 2017

    The position vector of the point $(4,5,6)$ is

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74. Q109 2017

    If $\overrightarrow{OA} = 2\vec{i} + 5\vec{j} - 2\vec{k}$ and…

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75. Q110 2017

    If $\vec{a} = \vec{i} + \vec{j} + 3\vec{k}; \vec{b} = 2\vec{i} + 3\vec{j} - 5\vec{k}$ then $\vec{a}.\vec{b} =$

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76. Q111 2017

    If $\vec{a}$ and $\vec{b}$ are mutually perpendicular then $3\vec{j}$

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77. Q113 2016

    $\left|-\vec{i}+2\vec{j}-3\vec{k}\right|=$

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78. Q114 2016

    If the position vectors of the points A and B be respectively (1, 2, 3) and (-3, -4, 0) then…

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79. 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 $\vec{a}\cdot\vec{b}$

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80. Q116 2016

    If $\vec{a}$ and $\vec{b}$ are perpendicular to each other then

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81. Q117 2016

    $\vec{i}\times\vec{j}=$

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82. Q118 2015

    The positive vector of the point $(1, 0, 2)$ is

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83. Q119 2015

    The modulus of $7\vec{i} - 2\vec{j} + \vec{k}$

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84. Q120 2015

    If O be the origin and $\overrightarrow{OP} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ and…

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85. 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

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86. Q122 2015

    If $\vec{a}\cdot\vec{b}=0$ then

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