← CBSE Class 12 PYQ

Three Dimensional Geometry

CBSE Class 12 · Mathematics · 37 past questions

Q1 2026

The length of perpendicular drawn from point $(2, 5, 7)$ on line $\frac{x}{1} = \frac{y}{0} = \frac{z}{0}$ is
Q2 2026

Assertion (A): Lines given by $x = py + q$, $z = ry + s$ and $x = p'y + q'$, $z = r'y + s'$ are perpendicular…
Q3 2026

Check whether the lines given by $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}$ and…
Q4 2026

Direction cosines of the line given by equations : $\frac{2x-1}{4} = \frac{1-y}{3} = \frac{-z}{6}$ are
Q5 2026

Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) based questions carrying 1 mark each.…
Q6 2026

Find the co-ordinates of the point on the line…
Q7 2026

A line passing through the points A(1, 2, 3) and B(5, 8, 11) intersects the line…
Q8 2026

If $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are direction cosines of lines $L_1$ and $L_2$ respectively and…
Q9 2026

Direction ratios of lines $l_1$ and $l_2$ are $<12, -3, 9>$ and $<4, q, -p>$ respectively. The values of p…
Q10 2026

If the lines $\frac{x-3}{1} = \frac{1-y}{1} = \frac{z+2}{p}$ and…
Q11 2026

Represent the equations of lines $l_1$ and $l_2$ in vector form and check whether they are intersecting or…
Q12 2025

Verify that lines given by $\vec r=(1-\lambda)\hat i+(\lambda-2)\hat j+(3-2\lambda)\hat k$ and…
Q13 2025

The line $x = 1 + 5\mu$, $y = -5 + \mu$, $z = -6 - 3\mu$ passes through which of the following point ?
Q14 2025

Find the shortest distance between the lines…
Q15 2025

If P is a point on the line segment joining $(3, 6, -1)$ and $(6, 2, -2)$ and y-coordinate of P is 4, then…
Q16 2024

The distance of point P(a, b, c) from y-axis is…
Q17 2024

Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
Q18 2024

The image of point $P(x, y, z)$ with respect to line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ is…
Q19 2024

If $\alpha$, $\beta$ and $\gamma$ are the angles which a line makes with positive directions of x, y and z…
Q20 2024

If a line makes an angle of $\dfrac{\pi}{4}$ with the positive directions of both x-axis and z-axis, then the…
Q21 2024

Find the equation of the line passing through the point of intersection of the lines…
Q22 2024

The coordinates of the foot of the perpendicular drawn from the point $(0, 1, 2)$ on the x-axis are given by…
Q23 2024

Direction ratios of a vector parallel to line $\dfrac{x-1}{2} = -y = \dfrac{2z+1}{6}$ are…
Q24 2024

If a line makes an angle of $30°$ with the positive direction of x-axis, $120°$ with the positive direction…
Q25 2024

Find the equation of the line which bisects the line segment joining points A(2, 3, 4) and B(4, 5, 8) and is…
Q26 2023

The value of $\lambda$ for which the angle between the lines…
Q27 2023

Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are…
Q28 2023

If the angle between the lines $\frac{x-5}{\alpha} = \frac{y+2}{-5} = \frac{z+\frac{24}{5}}{\beta}$ and…
Q29 2023

Find the value of b so that the lines $\frac{x-1}{2}=\frac{y-b}{3}=\frac{z-3}{4}$ and…
Q30 2023

Direction cosines of the line $\frac{x-1}{2} = \frac{1-y}{3} = \frac{2z-1}{12}$ are…
Q31 2023

Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are…
Q32 2023

Find the vector and the Cartesian equations of a line passing through the point $(1, 2, -4)$ and parallel to…
Q33 2023

Equation of a line passing through point (1, 1, 1) and parallel to z-axis is
Q34 2023

ASSERTION-REASON BASED QUESTIONS…
Q35 2023

Find the coordinates of points on line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z + 1}{2}$ which are at a…
Q36 2022

Find the values of $\lambda$, for which the distance of point $(2, 1, \lambda)$ from plane $3x+5y+4z=11$ is…
Q37 2022

Find the vector equation of the plane passing through the intersection of the planes…