Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

28 of 122 · show all

1. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set J2026 Set B

   $|\vec{a}|=2,\ |\vec{b}|=3,\ \vec{a}\cdot\vec{b}=4 \Rightarrow |\vec{a}-\vec{b}|=$

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2. 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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3. Q13 2026 Set D

   $|\vec{a}| = 2, |\vec{b}| = 3, \vec{a}\cdot\vec{b} = 4 \Rightarrow |\vec{a}-\vec{b}| =$

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4. Q15 2026 Set D2026 Set H

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

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5. Q17 2026 Set E

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

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6. Q24 2025

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

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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. 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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9. Q40 2025 Set A2024 Set D2024 Set J

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

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10. Q47 2025 Set E

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

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11. 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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12. 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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13. Q59 2024 Set J2018

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

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14. 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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15. Q64 2023

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

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16. Q70 20232023 Set E

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

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17. Q74 20232023 Set E

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

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18. Q82 2023 Set E

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

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19. Q85 2021 Set J2021 Set I

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

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20. Q99 2019 Set F

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

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21. Q104 2019 Set F2016

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

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22. Q108 2017

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

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23. Q109 2017

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

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24. Q113 2016

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

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25. 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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26. Q118 2015

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

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27. Q119 2015

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

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28. Q120 2015

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

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