Three Dimensional Geometry

Bihar Board Class 12 · Mathematics · 89 past questions

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1. Q13 20252024 Set J2024 Set D2019 Set F2017

   The direction cosines of z-axis are-

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2. Q14 2025

   The equation of $ZX$-plane is

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3. Q15 2025

   The distance between the points (–2, 6, 7) and (1, 2, 7) is

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4. Q16 2025

   If a line makes angle $30^0, 60^0$ and $90^0$ with the positive direction of $x, y$ and $z$-axis…

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5. Q17 2025

   Direction ratios of two lines are $a_1,b_1,c_1$ and $a_2,b_2,c_2$ respectively. Both lines are parallel, if

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6. Q18 2025

   The direction cosines of the unit vector perpendicular to the plane…

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7. Q19 2025

   If direction ratios of a straight line are 2, −3, 5 then its direction cosines are

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8. Q20 2025

   The plane parallel to the Plane $2x - 3y + 7z = 9$ is

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9. Q21 2025

   If two planes $x - 3y + 2z = 10$ and $7x + y - \lambda z = 5$ are perpendicular to each other, then…

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10. Q22 2025

    If the lines $\frac{x+1}{a}=\frac{y-2}{b}=\frac{z-3}{c}$ and $\frac{x-2}{3}=\frac{y-5}{1}=\frac{z-6}{2}$ are…

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11. Q23 2025

    The angle between the planes $4x + 8y + z - 3 = 0$ and $y + z - 7 = 0$ is

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12. Q24 2025

    The distance of the plane $2x - y + z = 7$ from the point $(0, 0, 1)$ is

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13. Q25 2025

    Find the distance of the point $(a,b,c)$ from $X$-axis.

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14. Q26 2025

    Find the equation of a plane passing through the points $(3,0,0), (0,-1,0)$ and $(0,0,2)$.

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15. Q27 2025

    The foot of perpendicular drawn from the origin to a plane is $(2,-1,3)$. Find the equation of the plane.

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16. Q28 2025 Set A2025 Set E

    If the direction ratios of two parallel lines are 2, 7, 9 and 6, 21, $x$, then the value of $x$ is

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17. Q29 2025 Set A2025 Set E

    If the direction ratios of two parallel lines are $a, b, c$ and $x, y, z$, then $az =$

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18. Q30 2025 Set A2025 Set E

    The direction ratios of the straight line $\frac{x-19}{13}=\frac{y-17}{11}=\frac{z-15}{9}$ are

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19. Q31 2025 Set A2025 Set E

    Through which of the following points does the line $\frac{x-11}{12}=\frac{y-12}{13}=\frac{z+13}{14}$ pass ?

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20. Q32 2025 Set A2025 Set E

    If the direction ratios of two mutually perpendicular lines are 5, 2, 4 and 4, 8, $x$ then the value $x$ is

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21. Q33 2025 Set A2025 Set E

    Equation of a plane parallel to the plane $9x-8y+7z=10$ is

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22. Q34 2025 Set E

    Find the acute angle between the line $\frac{x}{1}=\frac{y}{3}=\frac{z}{0}$ and the plane $2x+y=5$.

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