Three Dimensional Geometry

JEE Advanced · Mathematics · 38 past questions

1. Q1 2026 Paper 1

   Let $P$ be the plane such that it contains the straight line $\frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1}$ and…

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2. Q2 2026 Paper 2

   Let $L$ be the straight line joining the points $P(1,2,-1)$ and $Q(2,3,1)$. Let $S$ be the foot of the…

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3. Q3 2025 Paper 1

   Let $L_1$ be the line of intersection of the planes given by the equations…

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4. Q4 2024 Paper 1

   Let $\mathbb{R}^3$ denote the three-dimensional space. Take two points $P=(1,2,3)$ and $Q=(4,2,7)$. Let…

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5. Q5 2024 Paper 1

   Let $\gamma \in \mathbb{R}$ be such that the lines $L_1: \frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3}$ and…

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6. Q6 2024 Paper 2

   A straight line drawn from the point $P(1,3,2)$, parallel to the line…

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7. Q7 2023 Paper 1

   Let $Q$ be the cube with the set of vertices $\{(x_1,x_2,x_3)\in\mathbb{R}^3:x_1,x_2,x_3\in\{0,1\}\}$. Let…

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8. Q8 2023 Paper 1

   Let $\ell_1$ and $\ell_2$ be the lines $\vec r_1=\lambda(\hat i+\hat j+\hat k)$ and…

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9. Q9 2022 Paper 1

   Let $P_1$ and $P_2$ be two planes given by…

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10. Q10 2022 Paper 1

    Let $S$ be the reflection of a point $Q$ with respect to the plane given by…

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11. Q11 2021 Paper 1

    Let $\alpha, \beta$ and $\gamma$ be real numbers such that the system of linear equations…

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12. Q12 2020 Paper 1

    Let $L_1$ and $L_2$ be the following straight lines.…

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13. Q13 2020 Paper 2

    Let $\alpha, \beta, \gamma, \delta$ be real numbers such that $\alpha^2 + \beta^2 + \gamma^2 \neq 0$ and…

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14. Q14 2019 Paper 1

    Let $L_1$ and $L_2$ denote the lines…

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15. Q15 2019 Paper 2

    Three lines…

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16. Q16 2018 Paper 1

    Let $P_1: 2x + y - z = 3$ and $P_2: x + 2y + z = 2$ be two planes. Then, which of the following statement(s)…

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17. Q17 2018 Paper 2

    Let $P$ be a point in the first octant, whose image $Q$ in the plane $x+y=3$ (that is, the line segment $PQ$…

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18. Q18 2017 Paper 2

    The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes…

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19. Q19 2016 Paper 1

    Consider a pyramid $OPQRS$ located in the first octant ($x \ge 0, y \ge 0, z \ge 0$) with $O$ as origin, and…

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20. Q20 2016 Paper 2

    Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the…

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21. Q21 2015 Paper 1

    In $\mathbb{R}^3$, consider the planes $P_1: y=0$ and $P_2: x+z=1$. Let $P_3$ be a plane, different from…

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22. Q22 2015 Paper 1

    In $\mathbb{R}^3$, let $L$ be a straight line passing through the origin. Suppose that all the points on $L$…

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23. Q23 2014 Paper 1

    From a point $P(\lambda,\lambda,\lambda)$, perpendiculars $PQ$ and $PR$ are drawn respectively on the lines…

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24. Q24 2013 Paper 1

    Perpendiculars are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane…

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25. Q25 2013 Paper 1

    A line $l$ passing through the origin is perpendicular to the lines…

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26. Q26 2013 Paper 2

    Consider the lines $L_1 : \frac{x-1}{2} = \frac{y}{-1} = \frac{z+3}{1}$…

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27. Q27 2012 Paper 1

    The point $P$ is the intersection of the straight line joining the points $Q(2,3,5)$ and $R(1,-1,4)$ with the…

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28. Q28 2012 Paper 2

    The equation of a plane passing through the line of intersection of the planes $x + 2y + 3z = 2$ and…

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29. Q29 2010 Paper 1

    Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to…

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30. Q30 2010 Paper 1

    If the distance between the plane $Ax-2y+z=d$ and the plane containing the lines…

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31. Q31 2010 Paper 2

    If the distance of the point $P(1, -2, 1)$ from the plane $x + 2y - 2z = \alpha$, where $\alpha > 0$, is $5$…

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32. Q32 2009 Paper 1

    Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line…

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33. Q33 2009 Paper 2

    A line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angles with the…

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34. Q34 2008 Paper 1

    Consider three planes…

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35. Q35 2008 Paper 2

    Paragraph for Question Nos. 17 to 19…

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36. Q36 2008 Paper 2

    Paragraph for Question Nos. 17 to 19…

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37. Q37 2008 Paper 2

    Paragraph for Question Nos. 17 to 19…

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38. Q38 2007 Paper 2

    Consider the planes $3x - 6y - 2z = 15$ and $2x + y - 2z = 5$.…

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