Three Dimensional Geometry PYQs - Last 10 Years

MHT CET / Mathematics / Algebra / 353 recent questions

MathematicsAlgebra2017-2026

All Three Dimensional Geometry PYQs Last 5 Years Create chapter test

Practice 353 MHT CET Mathematics questions from Three Dimensional Geometry. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

353

PYQs on Page

Mathematics / Algebra

2019-2026

Year Range

Based on indexed question metadata

280

Last 5 Years

2022-2026

353

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

2024

2025

2026

202178 max PYQs/year2026

Question Types

353PYQs

MCQ100%

Difficulty Mix

#1 Unknown353

280 in last 5 years353 in last 10 years

Last 10 Years Three Dimensional Geometry Questions

Showing 50 of 353 filtered questions.

1Three Dimensional Geometry

The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$, which is perpendicular to the plane $x-y+z=0$, is

2Three Dimensional Geometry

The foot of the perpendicular drawn from origin to a plane is $\mathrm{M}(2,1,-2)$, then vector equation of the plane is

3Three Dimensional Geometry

The perpendicular distance of the origin from the plane $2 x+y-2 z-18=0$ is

4Three Dimensional Geometry

If the volume of tetrahedron whose vertices are $A \equiv(1,-6,10), B \equiv(-1,-3,7), C \equiv(5,-1, k)$ and $D \equiv(7,-4,7)$ is 11 cu . units, then the value of $k$ is

5Three Dimensional Geometry

The area of the triangle with vertices $(1,2,0)$, $(1,0,2)$ and $(0,3,1)$ is

6Three Dimensional Geometry

If the lines $\frac{x+1}{-10}=\frac{y+k}{-1}=\frac{z-4}{1} \quad$ and $\frac{x+10}{-1}=\frac{y+1}{-3}=\frac{z-1}{4}$ intersect each other, then the value of $k$ is

7Three Dimensional Geometry

The equation of the line passing through the point $(3,1,2)$ and perpendicular to the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$ is

8Three Dimensional Geometry

The plane $2 x+3 y+4 z=1$ meets $X$-axis in $A$, Y -axis in B and Z -axis in C . Then the centroid of $\triangle A B C$ is

9Three Dimensional Geometry

Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line $\bar{r}=\hat{i}-\hat{j}+2 \hat{k}+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which the vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+3...

10Three Dimensional Geometry

If for some $\alpha \in \mathbb{R}$, the lines $\mathrm{L}_1: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\mathrm{L}_2: \frac{x+2}{\alpha}=\frac{y+1}{5-\alpha}=\frac{z+1}{1}$ are coplanar, then the line $L_2$ passes through the point

11Three Dimensional Geometry

The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=\mathrm{z}$ is __________ units.

12Three Dimensional Geometry

A variable plane passes through the fixed point $(3,2,1)$ and meets $X, Y$ and $Z$ axes at points $A$, B and C respectively. A plane is drawn parallel to YZ - plane through A , a second plane is drawn parallel to ZX -plan through B , a thir...

13Three Dimensional Geometry

If the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{-1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then k is equal to

14Three Dimensional Geometry

Equation of the plane, through the points $(-1,2,-2)$ and $(-1,3,2)$ and perpendicular to $y \mathrm{z}$ - plane, is

15Three Dimensional Geometry

If the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lies in the plane $x+3 y-\alpha z+\beta=0$, then $(\alpha, \beta)=$

16Three Dimensional Geometry

If the line, $\frac{x-3}{2}=\frac{y+2}{1}=\frac{z+4}{3}$ lies in the plane, $\ell x+m y-z=9$, then $\ell^2+m^2$ is equal to

17Three Dimensional Geometry

The equation of the plane through the point $(2,-1,-3)$ and parallel to the lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and $\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}$ is

18Three Dimensional Geometry

The projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{CD}}$, where $A \equiv(2,-3,0), B \equiv(1,-4,-2), C \equiv(4,6,8)$ and $\mathrm{D} \equiv(7,0,10)$ is

19Three Dimensional Geometry

If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then the value of k is

20Three Dimensional Geometry

The vector equation of the plane passing through the point $\mathrm{A}(1,2,-1)$ and parallel to the vectors $2 \hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+3 \hat{k}$ is

21Three Dimensional Geometry

The shortest distance between lines $\bar{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$ and $\bar{r}=(2 \hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})$ is

22Three Dimensional Geometry

If the Cartesian equation of a line is \(6 x-2=3 y+1=2 z-2\), then the vector equation of the line is

23Three Dimensional Geometry

A vector \(\overrightarrow{\mathrm{n}}\) is inclined to \(\mathrm{X}\)-axis at \(45^{\circ}\), \(\mathrm{Y}\)-axis at \(60^{\circ}\) and at an acute angle to Z-axis If \(\overrightarrow{\mathrm{n}}\) is normal to a plane passing through the...

24Three Dimensional Geometry

The foot of the perpendicular drawn from the origin to the plane is \((4,-2,5)\), then the Cartesian equation of the plane is

25Three Dimensional Geometry

The equation of a plane, containing the line of intersection of the planes \(2 x-y-4=0\) and \(y+2 z-4=0\) and passing through the point \((2,1,0)\), is

26Three Dimensional Geometry

The co-ordinates of the point, where the line \(\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+5}{4}\) meets the plane \(2 x+4 y-\mathrm{z}=3\), are

27Three Dimensional Geometry

The shortest distance between the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}\) is

28Three Dimensional Geometry

If a line \(\mathrm{L}\) is the line of intersection of the planes \(2 x+3 y+z=1\) and \(x+3 y+2 z=2\). If line \(\mathrm{L}\) makes an angle \(\alpha\) with the positive \(\mathrm{X}\)-axis, then the value of \(\sec \alpha\) is

29Three Dimensional Geometry

Consider the lines \(\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{\mathrm{z}+1}{2}\)
\(\mathrm{L}_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{\mathrm{z}-3}{3}\), then the unit vector perpendicular to both \(\mathrm{L}_1\) and \(\mathrm{L}_2\) i...

30Three Dimensional Geometry

If the shortest distance between the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda}\) and \(\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}\) is \(\frac{1}{\sqrt{3}}\), then sum of possible values of \(\lambda\) is

31Three Dimensional Geometry

A line with positive direction cosines passes through the point \(\mathrm{P}(2,-1,2)\) and makes equal angles with the co-ordinate axes. The line meets the plane \(2 x+y+z=9\) at point \(\mathrm{Q}\). The length of the line segment \(P Q\) ...

32Three Dimensional Geometry

Equation of the plane passing through \((1,-1,2)\) and perpendicular to the planes \(x+2 y-2 z=4\) and \(3 x+2 y+z=6\) is

33Three Dimensional Geometry

The angle between the lines, whose direction cosines \(l, \mathrm{~m}, \mathrm{n}\) satisfy the equations \(l+\mathrm{m}+\mathrm{n}=0\) and \(2 l^2+2 \mathrm{~m}^2-\mathrm{n}^2=0\), is

34Three Dimensional Geometry

If \(\triangle \mathrm{ABC}\) is right angled at \(\mathrm{A}\), where \(A \equiv(4,2, x), \mathrm{B} \equiv(3,1,8)\) and \(C \equiv(2,-1,2)\), then the value of \(x\) is

35Three Dimensional Geometry

The length of the perpendicular drawn from the point \((1,2,3)\) to the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is

36Three Dimensional Geometry

A vector parallel to the line of intersection of the planes \(\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1\) and \(\bar{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2\) is

37Three Dimensional Geometry

If the lines \(\frac{x-\mathrm{k}}{2}=\frac{y+1}{3}=\frac{\mathrm{z}-1}{4}\) and \(\frac{x-3}{1}=\frac{y-\frac{9}{2}}{2}=\frac{\mathrm{z}}{1}\) intersect, then the value of \(\mathrm{k}\) is

38Three Dimensional Geometry

The mirror image of \(\mathrm{P}(2,4,-1)\) in the plane \(x-y+2 z-2=0\) is \((\mathrm{a}, \mathrm{b}, \mathrm{c})\), then the value of \(a+b+c\) is

39Three Dimensional Geometry

The distance of the point \((-1,-5,-10)\) from the point of intersection of the line \(\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\) and the plane \(x-y+z=5\) is

40Three Dimensional Geometry

If \(A(1,4,2)\) and \(C(5,-7,1)\) are two vertices of triangle \(A B C\) and \(G\left(\frac{4}{3}, 0, \frac{-2}{3}\right)\) is centroid of the triangle \(A B C\), then the mid point of side \(B C\) is

41Three Dimensional Geometry

The equation of the line passing through the point \((-1,3,-2)\) and perpendicular to each of the lines \(\frac{x}{1}=\frac{y}{2}=\frac{z}{3}\) and \(\frac{x+2}{-3}=\frac{y-1}{2}=\frac{z+1}{5}\) is

42Three Dimensional Geometry

A line \(\mathrm{L}_1\) passes through the point, whose p. v. (position vector) \(3 \hat{i}\), is parallel to the vector \(-\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\). Another line \(\mathrm{L}_2\) passes through the point having ...

43Three Dimensional Geometry

A line drawn from the point \(\mathrm{A}(1,3,2)\) parallel to the line \(\frac{x}{2}=\frac{y}{4}=\frac{z}{1}\), intersects the plane \(3 x+y+2 z=5\) in point \(\mathrm{B}\), then co-ordinates of point \(\mathrm{B}\) are

44Three Dimensional Geometry

The distance of the point \((1,6,2)\) from the point of intersection of the line \(\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\) and the plane \(x-y+z=16\) is

45Three Dimensional Geometry

The foot of the perpendicular from the point \((1,2,3)\) on the line \(\mathbf{r}=(6 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+7 \hat{\mathbf{k}})+\lambda(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})\) has the coordinates

46Three Dimensional Geometry

The acute angle between the line joining the points \((2,1,-3),(-3,1,7)\) and a line parallel to \(\frac{x-1}{3}=\frac{y}{4}=\frac{z+3}{5}\) through the point \((-1,0,4)\) is

47Three Dimensional Geometry

The incentre of the \(\triangle A B C\), whose vertices are \(A(0,2,1), B(-2,0,0)\) and \(C(-2,0,2)\), is

48Three Dimensional Geometry

A plane is parallel to two lines whose direction ratios are \(2,0,-2\) and \(-2,2,0\) and it contains the point \((2,2,2)\). If it cuts coordinate axes at \(A, B, C\), then the volume of the tetrahedron \(O A B C\) (in cubic units) is

49Three Dimensional Geometry

A tetrahedron has vertices at \(P(2,1,3), Q(-1,1,2), R(1,2,1)\) and \(O(0,0,0)\), then angle between the faces \(O P Q\) and \(P Q R\) is

50Three Dimensional Geometry

If the line \(\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 \mathrm{p}}=\frac{y-5}{1}=\frac{6-\mathrm{z}}{5}\) are at right angles, then \(\mathrm{p}=\)