Three Dimensional Geometry

CBSE Class 12 · Mathematics · 37 past questions

19 of 37 · show all

1. Q2 2026

   Assertion (A): Lines given by $x = py + q$, $z = ry + s$ and $x = p'y + q'$, $z = r'y + s'$ are perpendicular…

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2. Q3 2026

   Check whether the lines given by $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}$ and…

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3. Q4 2026

   Direction cosines of the line given by equations : $\frac{2x-1}{4} = \frac{1-y}{3} = \frac{-z}{6}$ are

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4. Q10 2026

   If the lines $\frac{x-3}{1} = \frac{1-y}{1} = \frac{z+2}{p}$ and…

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5. Q11 2026

   Represent the equations of lines $l_1$ and $l_2$ in vector form and check whether they are intersecting or…

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6. Q12 2025

   Verify that lines given by $\vec r=(1-\lambda)\hat i+(\lambda-2)\hat j+(3-2\lambda)\hat k$ and…

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7. Q14 2025

   Find the shortest distance between the lines…

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8. Q15 2025

   If P is a point on the line segment joining $(3, 6, -1)$ and $(6, 2, -2)$ and y-coordinate of P is 4, then…

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9. Q21 2024

   Find the equation of the line passing through the point of intersection of the lines…

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10. Q25 2024

    Find the equation of the line which bisects the line segment joining points A(2, 3, 4) and B(4, 5, 8) and is…

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11. Q27 2023

    Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are…

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12. Q28 2023

    If the angle between the lines $\frac{x-5}{\alpha} = \frac{y+2}{-5} = \frac{z+\frac{24}{5}}{\beta}$ and…

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13. Q29 2023

    Find the value of b so that the lines $\frac{x-1}{2}=\frac{y-b}{3}=\frac{z-3}{4}$ and…

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14. Q30 2023

    Direction cosines of the line $\frac{x-1}{2} = \frac{1-y}{3} = \frac{2z-1}{12}$ are…

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15. Q31 2023

    Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are…

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16. Q32 2023

    Find the vector and the Cartesian equations of a line passing through the point $(1, 2, -4)$ and parallel to…

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17. Q34 2023

    ASSERTION-REASON BASED QUESTIONS…

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18. Q35 2023

    Find the coordinates of points on line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z + 1}{2}$ which are at a…

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19. Q37 2022

    Find the vector equation of the plane passing through the intersection of the planes…

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