Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

34 of 122 · show all

1. 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 $|\vec{a}\times\vec{b}| =$

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2. 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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3. 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…

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4. 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…

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5. 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

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6. 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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7. 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…

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8. 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…

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9. 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…

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10. 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 $|\vec{a}\times\vec{b}|=$

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11. Q27 2025

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

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12. 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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13. 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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14. 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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15. Q37 2025

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

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16. Q48 2025 Set E

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

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17. Q50 2024 Set D2024 Set J

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

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18. 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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19. 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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20. Q55 2024 Set D

    Evaluate: $(\vec i-3\vec j+4\vec k)\cdot[(2\vec i-\vec j)\times(\vec j+\vec k)]$.

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21. Q58 2024 Set D2024 Set J

    $\vec{a}\times(\vec{b}+\vec{c})+\vec{b}\times(\vec{c}+\vec{a})+\vec{c}\times(\vec{a}+\vec{b}) =$

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22. 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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23. Q62 2024 Set J

    Evaluate : $(\vec i-3\vec j+4\vec k)\cdot\left[(2\vec i-\vec j)\times(\vec j+\vec k)\right]$.

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24. Q65 2023

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

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25. Q73 2023

    $(3\vec{k}-7\vec{i})\times 2\vec{k}=$

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26. Q75 20232023 Set E

    $(10\vec{i}+\vec{j}+\vec{k}) \times (-4\vec{i}+7\vec{j}-11\vec{k}) =$

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27. Q80 2023 Set E

    $(3\vec k-7\vec i)\times2\vec k=$

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28. 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

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29. 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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30. 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 $\vec{a}\times\vec{b}$

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31. 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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32. Q106 2018

    …

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33. Q107 2018

    Find the value of P, if: $(2\vec i+6\vec j+27\vec k)\times(\vec i+3\vec j+p\vec k)=\vec 0$

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34. Q112 2017

    If $\vec{a} = \hat{i} - 2\hat{j} - 3\hat{k}$; $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ and…

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