Three Dimensional Geometry

Bihar Board Class 12 · Mathematics · 89 past questions

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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

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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 $\lambda =$

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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…

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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…

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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…

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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 $6x-3y+9z-3=0$.

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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

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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…

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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…

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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…

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11. 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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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

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