Three Dimensional Geometry PYQs - Last 5 Years

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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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Last 5 Years Three Dimensional Geometry Questions

Showing 50 of 280 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 \(\mathrm{p}=\)