Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

27 of 122 · show all

1. Q22 2025

   If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that…

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2. Q23 2025

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

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3. Q24 2025

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

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4. Q25 2025

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

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5. Q26 2025

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

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6. Q27 2025

   $(\hat{j}+2\hat{k}) \times (\hat{i}+2\hat{j}) =$

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7. 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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8. Q29 2025

   If $\vec a = 2\hat\imath+3\hat\jmath+4\hat k,\vec b = -\hat\jmath-2\hat k$ then $|\vec a \times \vec b| =$

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9. 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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10. Q31 2025

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

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11. Q32 2025

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

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12. Q33 2025

    If $|\vec{a}| = 3, |\vec{b}| = \frac{\sqrt{2}}{3}$ and $\vec{a} \times \vec{b}$ is a unit vector then angle…

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13. Q34 2025

    …

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14. Q35 2025

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

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15. Q36 2025

    If $\vec{a} = \hat{\imath}+\hat{\jmath}+2\hat{k}$ and $\vec{b} = 2\hat{\imath}+\hat{\jmath}+2\hat{k}$ then…

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16. Q37 2025

    Find vector $\vec{v}$ which is perpendicular to $(2\hat{\imath}-\hat{\jmath}+2\hat{k})$ and…

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17. Q38 2025

    If $\vec{a} = \hat{i}-\hat{j}+\hat{k}$ and $\vec{b} = \hat{j}-\hat{k}$ then find $\vec{c}$ such that…

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18. Q39 2025 Set A2025 Set E

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

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19. Q40 2025 Set A2024 Set D2024 Set J

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

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20. 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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21. Q42 2025 Set A2025 Set E

    …

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22. 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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23. Q44 2025 Set A2025 Set E

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

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24. 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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25. Q46 2025 Set A2025 Set E

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

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26. Q47 2025 Set E

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

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27. Q48 2025 Set E

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

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