Three Dimensional Geometry

Bihar Board Class 12 · Mathematics · 89 past questions

20 of 89 · show all

1. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   If the direction cosines of two straight lines are $l_1, m_1, n_1$ and $l_2, m_2, n_2$ then the cosine of the…

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2. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   Find the value of $p$ so that the straight lines $\frac{x-1}{-1} = \frac{y+3}{p} = \frac{z-7}{2}$ and…

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3. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set J2026 Set D

   The angle between the straight lines $\frac{x-2}{2}=\frac{y-1}{7}=\frac{z+3}{-3}$ and…

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4. Q11 2026 Set B

   The angle between the straight lines $\frac{x-2}{2}=\frac{y-1}{7}=\frac{z+3}{-3}$ and…

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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. 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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7. 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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8. 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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9. 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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10. Q41 2024 Set D2024 Set J

    If the line $\frac{x-3}{a}=\frac{y-4}{b}=\frac{z-5}{c}$ is parallel to the line…

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11. Q42 2024 Set D2024 Set J

    Find the value of $p$ so that the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+17}{p}$ and…

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12. Q43 2024 Set D2024 Set J2016

    The direction ratios of two straight lines are $l,m,n$ and $l_1,m_1,n_1$. The lines will be perpendicular to…

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13. Q46 20232023 Set E

    If the direction ratios of two parallel lines are x, 5, 3 and 20, 10, 6 then the value of x is.

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14. 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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15. Q48 20232023 Set E

    If the direction ratios of two mutually perpendicular lines are 2, 3, 5 and x, y, 4 then $2x+3y=$

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16. 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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17. Q64 2021 Set J2021 Set I

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

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18. Q71 2017

    Let $l_1,m_1,n_1$ and $l_2,m_2,n_2$ be the direction cosines of two st-lines both the lines are perpendicular…

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19. Q80 2016

    The lines $\frac{x-1}{l}=\frac{y+2}{m}=\frac{z-4}{n}$ and $\frac{x+3}{2}=\frac{y-4}{3}=\frac{z}{6}$ are…

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20. Q85 2015

    If the direction cosines of the two straight lines are $l_1,m_1,n_1$ and $l_2,m_2,n_2$ then the cosine of the…

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