Vector Algebra

Bihar Board Class 12 · Mathematics · 122 past questions

18 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. 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…

   Try it →
3. Q12 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D2021 Set I

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

   Try it →
4. Q40 2025 Set A2024 Set D2024 Set J

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

   Try it →
5. 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…

   Try it →
6. Q50 2024 Set D2024 Set J

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

   Try it →
7. 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

   Try it →
8. Q52 2024 Set D2024 Set J

   $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| \Rightarrow$

   Try it →
9. 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

   Try it →
10. 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…

    Try it →
11. Q55 2024 Set D

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

    Try it →
12. Q56 2024 Set D2024 Set J20162015

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

    Try it →
13. Q57 2024 Set D2024 Set J

    $(4\vec{i}+3\vec{j}+3\vec{k})\cdot(6\vec{i}-4\vec{j}+\vec{k})=$

    Try it →
14. 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 →
15. Q59 2024 Set J2018

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

    Try it →
16. 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

    Try it →
17. 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…

    Try it →
18. Q62 2024 Set J

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

    Try it →