Three Dimensional Geometry

Bihar Board Class 12 · Mathematics · 89 past questions

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1. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set J2026 Set D

   Find the distance between the planes $2x-y+3z+4=0$ and $6x-3y+9z-3=0$.

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2. Q18 2025

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

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3. Q23 2025

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

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4. 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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5. 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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6. Q39 2024 Set D2024 Set J

   The angle between two planes $2x+y-2z=5$ and $3x-6y-2z=7$ is

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7. Q45 2024 Set J

   Find the distance between the planes $x - 2y + 2z = 6$ and $3x - 6y + 6z = 2$.

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8. Q47 20232023 Set E

   If the direction ratios of two parallel lines are $a_1, b_1, c_1$ and $a_2, b_2, c_2$ then…

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9. Q57 20232023 Set E

   Through which of the following points does the straight line…

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10. Q60 2023 Set E

    Find the acute angle between the lines $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and…

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11. Q64 2021 Set J2021 Set I

    The angle between the straight lines $2x=3y=-z$ and $6x=-y=-4z$ is

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12. Q70 2018

    Prove by direction numbers, that the points $(1,-1,3)$, $(2,-4,5)$ and $(5,-13,11)$ are in a straight line.

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13. Q82 2016

    Find the co-ordinates of the point where the line joining the points P(1, -2, 3) and Q(4, 7, 8) cuts the…

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