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← CBSE Class 12 PYQ

Vector Algebra

CBSE Class 12 · Mathematics · 46 past questions

  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…
  2. Q2 2026
    The value of m for which the points with position vectors $-\hat{i} - \hat{j} + 2\hat{k}$…
  3. Q3 2026
    If $|\vec{a}| = 8$, $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$, then the value of…
  4. Q4 2026
    Find the vector of magnitude 14 in the direction of $\overrightarrow{QP}$, where P and Q are the points (1…
  5. 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…
  6. Q6 2026
    If $|\vec{a}| = 5$ and $-2 \le \lambda \le 1$, then the sum of greatest and the smallest value of…
  7. Q7 2026
    Vector of magnitude 3 making equal angles with $x$ and $y$ axes and perpendicular to $z$ axis is
  8. Q8 2026
    Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) based questions carrying 1 mark each.…
  9. Q9 2026
    If $\overrightarrow{AB} = \hat{j} + \hat{k}$ and $\overrightarrow{AC} = 3\hat{i} - \hat{j} + 4\hat{k}$…
  10. Q10 2026
    For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true ?
  11. Q11 2026
    If $(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 198$ and $|\vec{a}| = 10|\vec{b}|$, then…
  12. Q12 2026
    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
  13. Q13 2026
    If for two unit vectors $\vec{a}$ and $\vec{b}$, $|\vec{a} + 2\vec{b}| = |2\vec{a} - \vec{b}|$, then find the…
  14. Q14 2025
    If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, $|\vec{a}| = \sqrt{37}$, $|\vec{b}| = 3$ and $|\vec{c}| = 4$…
  15. Q15 2025
    The diagonals of a parallelogram are given by $\vec a = 2\hat i - \hat j + \hat k$ and…
  16. Q16 2025
    The projection vector of vector $\vec{a}$ on vector $\vec{b}$ is
  17. Q17 2025
    The equation of a line parallel to the vector $3\hat{i} + \hat{j} + 2\hat{k}$ and passing through the point…
  18. Q18 2025
    Let $\vec{p}$ and $\vec{q}$ be two unit vectors and $\alpha$ be the angle between them. Then…
  19. Q19 2025
    If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors, then find x, such that…
  20. Q20 2025
    If the sides AB and AC of $\triangle ABC$ are represented by vectors $\hat{j} + \hat{k}$ and…
  21. Q21 2025
    Show that the area of a parallelogram whose diagonals are represented by $\vec{a}$ and $\vec{b}$ is given by…
  22. Q22 2024
    Let $\theta$ be the angle between two unit vectors $\hat{a}$ and $\hat{b}$ such that…
  23. Q23 2024
    The vector with terminal point A (2, – 3, 5) and initial point B (3, – 4, 7) is…
  24. Q24 2024
    In the given figure, ABCD is a parallelogram. If $\overrightarrow{AB} = 2\hat{i} - 4\hat{j} + 5\hat{k}$ and… (with a figure)
  25. 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…
  26. Q26 2024
    If $|\vec{a}| = 2$ and $-3 \le k \le 2$, then $|k\vec{a}| \in$…
  27. Q27 2024
    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
  28. Q28 2024
    Find the position vector of point C which divides the line segment joining points A and B having position…
  29. Q29 2024
    Let $\vec{a}$ and $\vec{b}$ be two non-zero vectors.…
  30. Q30 2024
    For any two vectors $\vec a$ and $\vec b$, which of the following statements is always true ?
  31. Q31 2024
    The unit vector perpendicular to both vectors $\hat{i} + \hat{k}$ and $\hat{i} - \hat{k}$ is…
  32. Q32 2024
    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
  33. Q33 2024
    The position vectors of vertices of $\Delta$ ABC are $A(2\hat{i} - \hat{j} + \hat{k})$…
  34. Q34 2023
    If a vector makes an angle of $\frac{\pi}{4}$ with the positive directions of both x-axis and y-axis, then…
  35. 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…
  36. Q36 2023
    In $\Delta$ ABC, $\overrightarrow{AB} = \hat{i} + \hat{j} + 2\hat{k}$ and…
  37. Q37 2023
    If $\vec{r} = 3\hat{i} - 2\hat{j} + 6\hat{k}$, find the value of…
  38. Q38 2023
    The value of p for which the vectors $2\hat{i} + p\hat{j} + \hat{k}$ and $-4\hat{i} - 6\hat{j} + 26\hat{k}$…
  39. Q39 2023
    The value of $(\hat{i} \times \hat{j}) \cdot \hat{j} + (\hat{j} \times \hat{i}) \cdot \hat{k}$ is…
  40. 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…
  41. Q41 2023
    Find all the vectors of magnitude $3\sqrt{3}$ which are collinear to vector $\hat{i} + \hat{j} + \hat{k}$.
  42. Q42 2023
    Unit vector along $\overrightarrow{PQ}$, where coordinates of P and Q respectively are (2, 1, $-1$) and (4…
  43. 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…
  44. Q44 2023
    Projection of vector $2\hat{i}+3\hat{j}$ on the vector $3\hat{i}-2\hat{j}$ is
  45. Q45 2023
    If $\vec{a}, \vec{b}, \vec{c}$ are three non-zero unequal vectors such that…
  46. Q46 2022
    In a parallelogram PQRS, $\overrightarrow{PQ} = 3\hat{i} - 2\hat{j} + 2\hat{k}$ and…