Vector Algebra

JEE Advanced · Mathematics · 44 past questions

30 of 44 · show all

1. Q1 2026 Paper 2

   Let $\vec{a}, \vec{b}$ be two vectors, and let $P, Q$ and $R$ be the points with position vectors $\vec{a}$…

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2. Q2 2025 Paper 1

   For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to…

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3. Q4 2024 Paper 1

   Let…

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4. Q5 2024 Paper 2

   Let $\vec p=2\hat i+\hat j+3\hat k$ and $\vec q=\hat i-\hat j+\hat k$. If for some real numbers…

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5. Q7 2023 Paper 2

   Let the position vectors of the points $P, Q, R$ and $S$ be $\vec a=\hat i+2\hat j-5\hat k$…

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6. Q10 2021 Paper 2

   Let $O$ be the origin and $\overrightarrow{OA}=2\hat i+2\hat j+\hat k$…

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7. Q12 2020 Paper 2

   Let $a$ and $b$ be positive real numbers. Suppose $\overrightarrow{PQ} = a\hat{i} + b\hat{j}$ and…

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8. Q13 2019 Paper 1

   Three lines are given by…

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9. Q14 2019 Paper 2

   Let $\vec a = 2\hat\imath+\hat\jmath-\hat k$ and $\vec b=\hat\imath+2\hat\jmath+\hat k$ be two vectors.…

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10. Q15 2018 Paper 1

    Let $\vec a$ and $\vec b$ be two unit vectors such that $\vec a\cdot\vec b=0$. For some $x,y\in\mathbb{R}$…

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11. Q16 2018 Paper 2

    Consider the cube in the first octant with sides $OP$, $OQ$ and $OR$ of length 1, along the $x$-axis…

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12. Q17 2017 Paper 2

    Let $O$ be the origin and let $PQR$ be an arbitrary triangle. The point $S$ is such that…

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13. Q20 2015 Paper 1

    Let $\Delta PQR$ be a triangle. Let $\vec a=\overrightarrow{QR}$, $\vec b=\overrightarrow{RP}$ and…

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14. Q21 2015 Paper 1

    Match the entries in Column I with the entries in Column II.

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15. Q22 2015 Paper 1

    Match the entries in Column I with the values in Column II.

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16. Q23 2015 Paper 2

    Suppose that $\vec{p}$, $\vec{q}$ and $\vec{r}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the…

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17. Q26 2013 Paper 1

    Let $\overrightarrow{PR}=3\hat i+\hat j-2\hat k$ and $\overrightarrow{SQ}=\hat i-3\hat j-4\hat k$ determine…

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18. Q27 2013 Paper 2

    Two lines $L_1 : x = 5, \frac{y}{3-\alpha} = \frac{z}{-2}$ and…

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19. Q28 2013 Paper 2

    Match List – I with List – II and select the correct answer using the code given below the lists…

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20. Q29 2012 Paper 1

    If $\vec a, \vec b$ and $\vec c$ are unit vectors satisfying…

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21. Q30 2012 Paper 2

    If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}| = \sqrt{29}$ and…

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22. Q31 2012 Paper 2

    If the straight lines $\frac{x-1}{2}=\frac{y+1}{k}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$…

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23. Q32 2011 Paper 1

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

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24. Q34 2011 Paper 2

    Let $\vec a=-\hat i-\hat k$, $\vec b=-\hat i+\hat j$ and $\vec c=\hat i+2\hat j+3\hat k$ be three given…

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25. Q36 2010 Paper 1

    If $\vec a$ and $\vec b$ are vectors in space given by $\vec a=\frac{\hat i-2\hat j}{\sqrt5}$ and…

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26. Q37 2010 Paper 2

    Two adjacent sides of a parallelogram $ABCD$ are given by…

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27. Q38 2010 Paper 2

    Match the statements in Column-I with the values in Column-II.

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28. Q39 2009 Paper 1

    If $\vec a,\vec b,\vec c$ and $\vec d$ are unit vectors such that…

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29. Q41 2008 Paper 2

    Let two non-collinear unit vectors $\hat a$ and $\hat b$ form an acute angle. A point $P$ moves so that at…

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30. Q43 2007 Paper 1

    Let the vectors $\vec{PQ}$, $\vec{QR}$, $\vec{RS}$, $\vec{ST}$, $\vec{TU}$ and $\vec{UP}$ represent the sides…

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