Vector Algebra

CBSE Class 12 · Mathematics · 46 past questions

24 of 46 · show all

1. Q1 2026

   The value of p for which vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $2\hat{i} - p\hat{j} + \hat{k}$ are…

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2. Q5 2026

   Vectors $\vec{a} = 3\hat{i} - 2\hat{j} + 2\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{k}$ represent the two…

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3. Q6 2026

   If $|\vec{a}| = 5$ and $-2 \le \lambda \le 1$, then the sum of greatest and the smallest value of…

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4. Q12 2026

   Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…

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5. Q16 2025

   The projection vector of vector $\vec{a}$ on vector $\vec{b}$ is

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6. Q17 2025

   The equation of a line parallel to the vector $3\hat{i} + \hat{j} + 2\hat{k}$ and passing through the point…

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7. Q22 2024

   Let $\theta$ be the angle between two unit vectors $\hat{a}$ and $\hat{b}$ such that…

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8. Q23 2024

   The vector with terminal point A (2, – 3, 5) and initial point B (3, – 4, 7) is…

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9. Q25 2024

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

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10. Q26 2024

    If $|\vec{a}| = 2$ and $-3 \le k \le 2$, then $|k\vec{a}| \in$…

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11. Q29 2024

    Let $\vec{a}$ and $\vec{b}$ be two non-zero vectors.…

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12. Q31 2024

    The unit vector perpendicular to both vectors $\hat{i} + \hat{k}$ and $\hat{i} - \hat{k}$ is…

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13. Q32 2024

    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…

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14. Q35 2023

    $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that the projection of $\vec{a}$ on $\vec{b}$ is 0. The…

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15. Q36 2023

    In $\Delta$ ABC, $\overrightarrow{AB} = \hat{i} + \hat{j} + 2\hat{k}$ and…

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16. Q38 2023

    The value of p for which the vectors $2\hat{i} + p\hat{j} + \hat{k}$ and $-4\hat{i} - 6\hat{j} + 26\hat{k}$…

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17. Q39 2023

    The value of $(\hat{i} \times \hat{j}) \cdot \hat{j} + (\hat{j} \times \hat{i}) \cdot \hat{k}$ is…

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18. Q40 2023

    If $\vec{a} + \vec{b} = \hat{i}$ and $\vec{a} = 2\hat{i} - 2\hat{j} + 2\hat{k}$, then $|\vec{b}|$ equals…

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19. Q41 2023

    Find all the vectors of magnitude $3\sqrt{3}$ which are collinear to vector $\hat{i} + \hat{j} + \hat{k}$.

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20. Q42 2023

    Unit vector along $\overrightarrow{PQ}$, where coordinates of P and Q respectively are (2, 1, $-1$) and (4…

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21. Q43 2023

    Position vector of the mid-point of line segment AB is $3\hat{i}+2\hat{j}-3\hat{k}$. If position vector of…

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22. Q44 2023

    Projection of vector $2\hat{i}+3\hat{j}$ on the vector $3\hat{i}-2\hat{j}$ is

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23. Q45 2023

    If $\vec{a}, \vec{b}, \vec{c}$ are three non-zero unequal vectors such that…

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24. Q46 2022

    In a parallelogram PQRS, $\overrightarrow{PQ} = 3\hat{i} - 2\hat{j} + 2\hat{k}$ and…

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