Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

27 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

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

   Try it →
2. 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 $|\vec{a}\times\vec{b}| =$

   Try it →
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…

   Try it →
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…

   Try it →
5. 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…

   Try it →
6. Q16 2026 Set E

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

   Try it →
7. 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…

   Try it →
8. 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…

   Try it →
9. 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 $|\vec{a}\times\vec{b}|=$

   Try it →
10. Q26 2025

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

    Try it →
11. Q27 2025

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

    Try it →
12. Q29 2025

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

    Try it →
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…

    Try it →
14. Q37 2025

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

    Try it →
15. Q38 2025

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

    Try it →
16. Q46 2025 Set A2025 Set E

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

    Try it →
17. Q50 2024 Set D2024 Set J

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

    Try it →
18. Q58 2024 Set D2024 Set J

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

    Try it →
19. Q63 20232023 Set E2017

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

    Try it →
20. Q73 2023

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

    Try it →
21. Q75 20232023 Set E

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

    Try it →
22. Q80 2023 Set E

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

    Try it →
23. Q94 2021 Set J

    $\hat i\times\hat k=$

    Try it →
24. Q95 2021 Set J

    $\vec a\times\vec b=$

    Try it →
25. Q100 2019 Set F

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

    Try it →
26. 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 $\vec{a}\times\vec{b}$

    Try it →
27. Q117 2016

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

    Try it →