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← Bihar Board Class 12 PYQ

Three Dimensional Geometry

Bihar Board Class 12 · Mathematics · 89 past questions

  1. Q1 2026 Set A2026 Set D2026 Set F
    The distance of the plane $x+2y-2z=9$ from the point $(2, 3, -5)$ is
  2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    If two planes $x-4y+\lambda z+3=0$ and $2x+2y+3z=5$ are perpendicular to each other then $\lambda =$
  3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D
    If the line $\dfrac{x-x_1}{a_1}=\dfrac{y-y_1}{b_1}=\dfrac{z-z_1}{c_1}$ is parallel to the plane…
  4. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    The equation of the plane whose intercepts on the $x$, $y$ and $z$-axes are $-2$, $3$ and $4$ respectively…
  5. 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…
  6. 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 $6x-3y+9z-3=0$.
  7. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    The direction ratios of a straight line are 2, 6, $-3$. Then its direction cosines are
  8. 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…
  9. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    If a line makes angles $\alpha$, $\beta$ and $\gamma$ with the positive directions of $x$, $y$ and $z$ axes…
  10. 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…
  11. Q11 2026 Set B
    The angle between the straight lines $\frac{x-2}{2}=\frac{y-1}{7}=\frac{z+3}{-3}$ and…
  12. Q12 2026 Set H2026 Set E2026 Set C2026 Set J2026 Set B
    The distance of the plane $x+2y-2z=9$ from the point $(2,3,-5)$ is
  13. Q13 20252024 Set J2024 Set D2019 Set F2017
    The direction cosines of z-axis are-
  14. Q14 2025
    The equation of $ZX$-plane is
  15. Q15 2025
    The distance between the points (–2, 6, 7) and (1, 2, 7) is
  16. Q16 2025
    If a line makes angle $30^0, 60^0$ and $90^0$ with the positive direction of $x, y$ and $z$-axis…
  17. 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
  18. Q18 2025
    The direction cosines of the unit vector perpendicular to the plane…
  19. Q19 2025
    If direction ratios of a straight line are 2, −3, 5 then its direction cosines are
  20. Q20 2025
    The plane parallel to the Plane $2x - 3y + 7z = 9$ is
  21. Q21 2025
    If two planes $x - 3y + 2z = 10$ and $7x + y - \lambda z = 5$ are perpendicular to each other, then…
  22. 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…
  23. Q23 2025
    The angle between the planes $4x + 8y + z - 3 = 0$ and $y + z - 7 = 0$ is
  24. Q24 2025
    The distance of the plane $2x - y + z = 7$ from the point $(0, 0, 1)$ is
  25. Q25 2025
    Find the distance of the point $(a,b,c)$ from $X$-axis.
  26. Q26 2025
    Find the equation of a plane passing through the points $(3,0,0), (0,-1,0)$ and $(0,0,2)$.
  27. Q27 2025
    The foot of perpendicular drawn from the origin to a plane is $(2,-1,3)$. Find the equation of the plane.
  28. 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
  29. Q29 2025 Set A2025 Set E
    If the direction ratios of two parallel lines are $a, b, c$ and $x, y, z$, then $az =$
  30. 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
  31. 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 ?
  32. 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
  33. Q33 2025 Set A2025 Set E
    Equation of a plane parallel to the plane $9x-8y+7z=10$ is
  34. Q34 2025 Set E
    Find the acute angle between the line $\frac{x}{1}=\frac{y}{3}=\frac{z}{0}$ and the plane $2x+y=5$.
  35. Q35 2024 Set D2024 Set J2018
    The equation of the xy-plane is…
  36. Q36 2024 Set D2024 Set J
    The distance between the points $(4, 3, 7)$ and $(1, -1, -5)$ is
  37. Q37 2024 Set D2024 Set J
    The direction ratios of a straight line are 1, 3, 5. Then its direction cosines are
  38. Q38 2024 Set D2024 Set J
    The equation of the plane parallel to the plane $3x-5y+4z=11$ is
  39. Q39 2024 Set D2024 Set J
    The angle between two planes $2x+y-2z=5$ and $3x-6y-2z=7$ is
  40. Q40 2024 Set D2024 Set J
    If two planes $2x-4y+3z=5$ and $x+2y+\lambda z=12$ are mutually perpendicular to each other then $\lambda =$
  41. 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…
  42. 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…
  43. 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…
  44. Q44 2024 Set D2024 Set J
    The distance of the plane $x-2y+4z=9$ from the point $(2, 1, -1)$ is
  45. Q45 2024 Set J
    Find the distance between the planes $x - 2y + 2z = 6$ and $3x - 6y + 6z = 2$.
  46. 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.
  47. 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…
  48. Q48 20232023 Set E
    If the direction ratios of two mutually perpendicular lines are 2, 3, 5 and x, y, 4 then $2x+3y=$
  49. Q49 20232023 Set E
    If the direction cosines of a line be $\frac{4}{\sqrt{77}}, \frac{5}{\sqrt{77}}$ and $\frac{x}{\sqrt{77}}$…
  50. Q50 2023
    Distance of the plane 3x-4y+6z=11 from origin is
  51. Q51 20232023 Set E
    Equation of a plane parallel to the plane x-8y-9z=12 is
  52. Q52 20232023 Set E
    The intercept cut off on x-axis by the plane 3x+4y+5z=13 is
  53. Q53 20232023 Set E
    If the line $\frac{x}{-1} = \frac{y}{2} = \frac{z}{3}$ is parallel to the plane $ax+by+cz+d=0$ then
  54. Q54 2023
    If two planes $a_1x + b_1y + c_1z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$ are mutually perpendicular…
  55. Q55 20232023 Set E
    Direction ratios of the normal to the plane x+2y-3z+15=0 are
  56. Q56 20232023 Set E
    The direction ratios of the straight line $\dfrac{x+1}{3}=\dfrac{y-2}{3}=\dfrac{z-5}{6}$
  57. Q57 20232023 Set E
    Through which of the following points does the straight line…
  58. Q58 2023 Set E
    Distance of the plane $3x - 4y + 6z = 11$ from origin is
  59. Q59 2023 Set E
    If two planes $a_1x+b_1y+c_1z+d_1=0$ and $a_2x+b_2y+c_2z+d_2=0$ are mutually perpendicular then
  60. Q60 2023 Set E
    Find the acute angle between the lines $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and…
  61. Q61 2021 Set I
    The distance between $(-4, -3, 7)$ and $(-1, 1, -5)$ is
  62. Q62 2021 Set J2021 Set I
    Standard equation of the plane in intercept form is
  63. Q63 2021 Set J2021 Set I
    The distance of the point $(-3,-4,-5)$ from the origin is
  64. Q64 2021 Set J2021 Set I
    The angle between the straight lines $2x=3y=-z$ and $6x=-y=-4z$ is
  65. Q65 2021 Set J
    The distance between $(-4,-3,7)$ and $(-1,1,-5)$ is
  66. Q66 2019 Set F
    The distance of the point $(3,4,5)$ from x-axis is -
  67. Q67 2018
    The direction Cosines of y axis are…
  68. Q68 2018
    If two planes $-2x - 4y + 3z = 5$ and $x + 2y + \lambda z = 12$ are perpendicular to each other, then…
  69. Q69 2018
    The distance between (4,3,7) and (1,-1,-5) is…
  70. Q70 2018
    Prove by direction numbers, that the points $(1,-1,3)$, $(2,-4,5)$ and $(5,-13,11)$ are in a straight line.
  71. 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…
  72. Q72 2017
    let a,b,c be the direction ratios of a line then direction cosines are
  73. Q73 2017
    A line is passing through $(\alpha,\beta,\gamma)$ and its direction cosines are $l,m,n$ then the equations of…
  74. Q74 20172015
    The direction ratios of the normal to the plane $7x+4y-2z+5=0$ are
  75. Q75 20162015
    The direction cosines of the y-axis are
  76. Q76 2016
    l, m, n, are the direction cosines of a straight line them
  77. Q77 2016
    The distance between the points (4,3,7) and (1,-1,-5) is
  78. Q78 2016
    The direction between the points (4,3,7) and (1,-1,-5) is
  79. Q79 2016
    A line passing through (2, -1, 3) and its direction ratios are 3, -1, 2. The equation of the line is
  80. 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…
  81. Q81 2016
    The length of the perpendicular from the point (0,-1,3) to the plane $2x+y-2z+1=0$ his.
  82. 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…
  83. Q83 2015
    The direction ratios of the line joining the points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ are
  84. Q84 2015
    The co-ordinates of the midpoint of the line segment joining the points $(2,3,4)$ and $(8,-3,8)$ are
  85. 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…
  86. Q86 2015
    If the line $\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$ is parallel to the plane $ax+by+cz+d=0$, then
  87. Q87 2015
    If the planes $a_1x+b_1y+c_1z+d_1=0$ and $a_2x+b_2y+c_2z+d_2=0$
  88. Q88 2015
    The distance of the plane $2x-3y+6z+7=0$ from the point $(2,-3,-1)$
  89. Q89 2015
    Find the equation of the straight line perpendicular to the two lines…