Vector Algebra

JEE Advanced · Mathematics · 44 past questions

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 $\vec{a}$…

   Try it →
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…

   Try it →
3. Q3 2025 Paper 2

   Consider the vectors…

   Try it →
4. Q4 2024 Paper 1

   Let…

   Try it →
5. 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…

   Try it →
6. Q6 2023 Paper 1

   Let $P$ be the plane $\sqrt3x+2y+3z=16$ and let…

   Try it →
7. Q7 2023 Paper 2

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

   Try it →
8. Q8 2022 Paper 2

   Let $\hat{i}$, $\hat{j}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let…

   Try it →
9. Q9 2021 Paper 1

   Let $\vec u$, $\vec v$ and $\vec w$ be vectors in three-dimensional space, where $\vec u$ and $\vec v$ are…

   Try it →
10. Q10 2021 Paper 2

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

    Try it →
11. Q11 2020 Paper 1

    In a triangle $PQR$, let $\vec a=\overrightarrow{QR}$, $\vec b=\overrightarrow{RP}$ and…

    Try it →
12. Q12 2020 Paper 2

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

    Try it →
13. Q13 2019 Paper 1

    Three lines are given by…

    Try it →
14. 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.…

    Try it →
15. Q15 2018 Paper 1

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

    Try it →
16. Q16 2018 Paper 2

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

    Try it →
17. Q17 2017 Paper 2

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

    Try it →
18. Q18 2017 Paper 2

    Let $O$ be the origin, and $\overrightarrow{OX}, \overrightarrow{OY}, \overrightarrow{OZ}$ be three unit…

    Try it →
19. Q19 2016 Paper 2

    Let $\hat{u} = u_1\hat{i} + u_2\hat{j} + u_3\hat{k}$ be a unit vector in $\mathbb{R}^3$ and…

    Try it →
20. Q20 2015 Paper 1

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

    Try it →
21. Q21 2015 Paper 1

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

    Try it →
22. Q22 2015 Paper 1

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

    Try it →
23. Q23 2015 Paper 2

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

    Try it →
24. Q24 2014 Paper 1

    Let $\vec{x}$, $\vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between…

    Try it →
25. Q25 2014 Paper 1

    Let $\vec a,\vec b$ and $\vec c$ be three non-coplanar unit vectors such that the angle between every pair of…

    Try it →
26. 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…

    Try it →
27. Q27 2013 Paper 2

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

    Try it →
28. Q28 2013 Paper 2

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

    Try it →
29. Q29 2012 Paper 1

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

    Try it →
30. Q30 2012 Paper 2

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

    Try it →
31. Q31 2012 Paper 2

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

    Try it →
32. Q32 2011 Paper 1

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

    Try it →
33. Q33 2011 Paper 1

    The vector(s) which is/are coplanar with vectors $\hat{i}+\hat{j}+2\hat{k}$ and $\hat{i}+2\hat{j}+\hat{k}$…

    Try it →
34. 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…

    Try it →
35. Q35 2010 Paper 1

    Let P, Q, R and S be the points on the plane with position vectors $-2\hat{i}-\hat{j}$, $4\hat{i}$…

    Try it →
36. 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…

    Try it →
37. Q37 2010 Paper 2

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

    Try it →
38. Q38 2010 Paper 2

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

    Try it →
39. Q39 2009 Paper 1

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

    Try it →
40. Q40 2008 Paper 1

    The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors…

    Try it →
41. 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…

    Try it →
42. Q42 2007 Paper 1

    The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2\hat{i}+\hat{j}+\hat{k}$…

    Try it →
43. Q43 2007 Paper 1

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

    Try it →
44. Q44 2007 Paper 2

    Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$. Which one…

    Try it →