Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

45 of 122 · show all

1. 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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2. 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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3. 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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4. Q21 2026 Set J

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

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5. Q23 2025

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

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6. Q25 2025

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

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7. 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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8. Q32 2025

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

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9. Q35 2025

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

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10. Q39 2025 Set A2025 Set E

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

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11. 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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12. Q42 2025 Set A2025 Set E

    …

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13. 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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14. 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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15. Q48 2025 Set E

    Find the value of $x$, when the following vectors are perpendicular to one another…

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16. 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

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17. 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

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18. Q56 2024 Set D2024 Set J20162015

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

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19. 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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20. 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

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21. Q65 2023

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

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22. Q66 2023

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

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23. Q67 2023

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

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24. Q68 20232023 Set E

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

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25. Q69 2023

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

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26. Q71 20232023 Set E

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

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27. 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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28. Q76 2023

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

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29. Q77 2023 Set E

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

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30. Q78 2023 Set E

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

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31. Q79 2023 Set E

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

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32. Q81 2023 Set E

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

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33. Q83 2023 Set E2015

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

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34. Q88 2021 Set J2021 Set I

    $\hat{n}^2 =$

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35. Q89 2021 Set J2021 Set I2015

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

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36. Q96 2021 Set J2021 Set I

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

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37. Q98 2019 Set F

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

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38. 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…

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39. 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…

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40. 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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41. Q111 2017

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

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42. 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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43. Q116 2016

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

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44. 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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45. Q122 2015

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

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