Vector Algebra

CBSE Class 12 · Mathematics · 46 past questions

22 of 46 · show all

1. Q2 2026

   The value of m for which the points with position vectors $-\hat{i} - \hat{j} + 2\hat{k}$…

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2. Q3 2026

   If $|\vec{a}| = 8$, $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$, then the value of…

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3. Q4 2026

   Find the vector of magnitude 14 in the direction of $\overrightarrow{QP}$, where P and Q are the points (1…

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4. Q7 2026

   Vector of magnitude 3 making equal angles with $x$ and $y$ axes and perpendicular to $z$ axis is

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5. Q8 2026

   Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) based questions carrying 1 mark each.…

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6. Q9 2026

   If $\overrightarrow{AB} = \hat{j} + \hat{k}$ and $\overrightarrow{AC} = 3\hat{i} - \hat{j} + 4\hat{k}$…

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7. Q10 2026

   For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true ?

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8. Q11 2026

   If $(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 198$ and $|\vec{a}| = 10|\vec{b}|$, then…

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9. 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…

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10. Q14 2025

    If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, $|\vec{a}| = \sqrt{37}$, $|\vec{b}| = 3$ and $|\vec{c}| = 4$…

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11. Q15 2025

    The diagonals of a parallelogram are given by $\vec a = 2\hat i - \hat j + \hat k$ and…

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12. Q18 2025

    Let $\vec{p}$ and $\vec{q}$ be two unit vectors and $\alpha$ be the angle between them. Then…

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13. Q19 2025

    If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors, then find x, such that…

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14. Q20 2025

    If the sides AB and AC of $\triangle ABC$ are represented by vectors $\hat{j} + \hat{k}$ and…

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15. Q21 2025

    Show that the area of a parallelogram whose diagonals are represented by $\vec{a}$ and $\vec{b}$ is given by…

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16. 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)

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17. Q27 2024

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

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18. Q28 2024

    Find the position vector of point C which divides the line segment joining points A and B having position…

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19. Q30 2024

    For any two vectors $\vec a$ and $\vec b$, which of the following statements is always true ?

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20. Q33 2024

    The position vectors of vertices of $\Delta$ ABC are $A(2\hat{i} - \hat{j} + \hat{k})$…

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21. Q34 2023

    If a vector makes an angle of $\frac{\pi}{4}$ with the positive directions of both x-axis and y-axis, then…

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22. Q37 2023

    If $\vec{r} = 3\hat{i} - 2\hat{j} + 6\hat{k}$, find the value of…

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