Three Dimensional Geometry PYQs - Last 5 Years

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MathematicsAlgebra2022-2026

All Three Dimensional Geometry PYQs Last 10 Years Create chapter test

Practice 280 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.

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Mathematics / Algebra

2022-2026

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280

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2022-2026

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Last 5 Years Three Dimensional Geometry Questions

Showing 30 of 280 filtered questions.

1Three Dimensional Geometry

The distance of the point \(\mathrm{P}(-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) is

2Three Dimensional Geometry

The equation of the plane through \((-1,1,2)\) whose normal makes equal acute angles with co-ordinate axes is

3Three Dimensional Geometry

A plane is parallel to two lines whose direction ratios are \(1,0,-1\) and \(-1,1,0\) and it contains the point \((1,1,1)\). If it cuts the co-ordinate axes at \(\mathrm{A}, \mathrm{B}, \mathrm{C}\), then the volume of the tetrahedron $$\ma...

4Three Dimensional Geometry

The centroid of tetrahedron with vertices at \(\mathrm{A}(-1,2,3), \mathrm{B}(3,-2,1), \mathrm{C}(2,1,3)\) and \(\mathrm{D}(-1,-2,4)\) is

5Three Dimensional Geometry

Equation of plane containing the line \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\) and perpendicular to the plane containing the lines \(\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\) and \(\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\) is

6Three Dimensional Geometry

If the volume of tetrahedron, whose vertices are \(\mathrm{A}(1,2,3), \mathrm{B}(-3,-1,1), \mathrm{C}(2,1,3)\) and \(D(-1,2, x)\) is \(\frac{11}{6}\) cubic units, then the value of \(x\) is

7Three Dimensional Geometry

The length (in units) of the projection of the line segment, joining the points \((5,-1,4)\) and \((4,-1,3)\), on the plane \(x+y+z=7\) is

8Three Dimensional Geometry

The shortest distance (in units) between the lines \(\frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}\) and \(\bar{r}=(2 \hat{i}-2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+2 \hat{j})\) is

9Three Dimensional Geometry

The equation of the line, passing through \((1,2,3)\) and parallel to planes \(x-y+2 z=5\) and \(3 x+y+z=6\), is

10Three Dimensional Geometry

The vector equation of the line \(2 x+4=3 y+1=6 z-3\) is

11Three Dimensional Geometry

The lines \(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad\) and \(\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}\)

12Three Dimensional Geometry

A plane is parallel to two lines, whose direction ratios are \(1,0,-1\) and \(-1,1,0\) and it contains the point \((1,1,1)\). If it cuts co-ordinate axes \((\mathrm{X}, \mathrm{Y}, \mathrm{Z}\) - axes resp.) at $$\mathrm{A}, \mathrm{B}, \ma...

13Three Dimensional Geometry

The mirror image of the point \((1,2,3)\) in a plane is \(\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)\). Thus, the point _________ lies on this plane.

14Three Dimensional Geometry

If the direction cosines \(l, \mathrm{~m}, \mathrm{n}\) of two lines are connected by relations \(l-5 \mathrm{~m}+3 \mathrm{n}=0\) and \(7 l^2+5 \mathrm{~m}^2-3 \mathrm{n}^2=0\), then value of \(l+\mathrm{m}+\mathrm{n}\) is

15Three Dimensional Geometry

The angle between the line \(\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}\) and plane \(x-2 y-\lambda z=3\) is \(\cos ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)\), then value of \(\lambda\) is

16Three Dimensional Geometry

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

17Three Dimensional Geometry

If the line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}\) meets the plane \(x+2 y+3 z=15\) at the point \(P\), then the distance of \(\mathrm{P}\) from the origin is

18Three Dimensional Geometry

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

19Three Dimensional Geometry

\(\mathrm{ABC}\) is a triangle in a plane with vertices \(\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2)\) and \(\mathrm{C}(\lambda, 5, \mu)\). If median through \(\mathrm{A}\) is equally inclined to the co-ordinate axes, then value of $$\lambda+\mu...

20Three Dimensional Geometry

The co-ordinates of the point, where the line through \(A(3,4,1)\) and \(B(5,1,6)\) crosses the \(\mathrm{XZ}\)-plane, are

21Three Dimensional Geometry

Let \(\mathrm{P}\) be a plane passing through the points \((2,1,0),(4,1,1)\) and \((5,0,1)\) and \(R\) be the point \((2,1,6)\). Then image of \(R\) in the plane \(P\) is

22Three Dimensional Geometry

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 the value of \(\alpha^2+\alpha \beta+\beta^2\) is

23Three Dimensional Geometry

Two lines \(\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}\) and \(\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4} \quad\) intersect at the point R. Then reflection of \(\mathrm{R}\) in the \(x y\)-plane has co-ordinates

24Three Dimensional Geometry

The perpendicular distance of the origin from the plane \(x-3 y+4 z-6=0\) is

25Three Dimensional Geometry

The plane through the intersection of planes \(x+y+z=1\) and \(2 x+3 y-z+4=0\) and parallel to \(\mathrm{Y}\)-axis also passes through the point

26Three Dimensional Geometry

The equation of the plane passing through the points \((2,3,1),(4,-5,3)\) and parallel to \(X\)-axis is

27Three Dimensional Geometry

A tetrahedron has verticles \(P(1,2,1), Q(2,1,3), R(-1,1,2)\) and \(O(0,0,0)\). Then the angle between the faces \(O P Q\) and \(P Q R\) is

28Three Dimensional Geometry

The Cartesian equation of a line passing through \((1,2,3)\) and parallel to \(x-y+2 z=5\) and \(3 x+y+z=6\) is

29Three Dimensional Geometry

The distance between parallel lines \(\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}\) and \(\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}\) is :

30Three Dimensional Geometry

A line makes the same angle '\(\alpha\)' with each of the \(x\) and \(y\) axes. If the angle '\(\theta\)', which it makes with the \(z\)-axis, is such that \(\sin ^2 \theta=2 \sin ^2 \alpha\), then the angle \(\alpha\) is