Three Dimensional Geometry PYQs - Last 5 Years

COMEDK / Mathematics / Algebra / 34 recent questions

MathematicsAlgebra2022-2026

All Three Dimensional Geometry PYQs Last 10 Years Create chapter test

Practice 34 COMEDK 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.

34

PYQs on Page

Mathematics / Algebra

2022-2026

Year Range

Based on indexed question metadata

34

Last 5 Years

2022-2026

34

Last 10 Years

2017-2026

Recent Year Trend

2022

2023

2024

2025

2026

20229 max PYQs/year2026

Question Types

34PYQs

MCQ100%

Difficulty Mix

#1 Unknown34

34 in last 5 years34 in last 10 years

Last 5 Years Three Dimensional Geometry Questions

Showing 34 of 34 filtered questions.

1Three Dimensional Geometry

Let $\mathbf{P}$ be a point on the line $L_1: \frac{x-2}{2}=y+1=\frac{z-1}{2}$ such that its distance from the point $A(2,-1,1)$ is 6 units.
Given that $\boldsymbol{x}$-coordinate of $\mathbf{P}$ is greater than $\mathbf{2}$,
Find the coord...

2Three Dimensional Geometry

The angle between the two lines whose direction cosines satisfy the relations $\boldsymbol{l}+\boldsymbol{m}+\boldsymbol{n}=\mathbf{0}$ and $\boldsymbol{l}^{\mathbf{2}}=\boldsymbol{m}^{\mathbf{2}}+\boldsymbol{n}^{\mathbf{2}}$ is

3Three Dimensional Geometry

Let L be the foot of the perpendicular drawn from the point $P(5,3 k-7,-4)$ to the YZ - plane. If the distance of point L from the origin is $\sqrt{41}$ units, then the possible value of ' $\boldsymbol{k}$ ' is:

4Three Dimensional Geometry

$$ \begin{aligned} &\text { Consider two skew lines in 3D space. }\\ &M_1: \frac{x-1}{1}=\frac{2-y}{1}=\frac{z-5}{1} \text { and } M_2: \frac{x+3}{1}=\frac{y-7}{2}=\frac{z+4}{1} \end{aligned} $$
Let $L_1$ be the line of shortest distance (c...

5Three Dimensional Geometry

The equation of the perpendicular drawn from the point $A(6,1,3)$ to the line $\frac{x-1}{2}=\frac{2-y}{-1}=\frac{z-3}{2}$ is $\frac{x-6}{\boldsymbol{a}}=\frac{y-1}{\boldsymbol{b}}=\frac{z-3}{\boldsymbol{c}}$. If $\mathbf{a}, \mathbf{b}, \m...

6Three Dimensional Geometry

Consider the lines $L_1$ and $L_2$ given by the following vector equations:
$$ L_1: \vec{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(3 \hat{i}+\boldsymbol{t} \hat{j}) \quad L_2: \vec{r}=(4 \hat{i}+\boldsymbol{a} \hat{j}-\hat{k})+\mu(2 \hat{i}+3 \h...

7Three Dimensional Geometry

The value of $\lambda$ for which the angle between lines $\vec{r}=\hat{\imath}+\hat{\jmath}+\hat{k}+p(2 \hat{\imath}+\hat{\jmath}+2 \hat{k})$ and $\vec{r}=(1+q) \hat{\imath}+(1+q \lambda) \hat{\jmath}+(1+q) \hat{k}$ is $\frac{\pi}{2}$

8Three Dimensional Geometry

P is a point on the line joining the points $(3,5,-1)$ and $(6,3,-2)$. If $y$ coordinate of point P is 2 , then $x$ coordinate will be

9Three Dimensional Geometry

The image of a point $P(3,5,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is $P^{\prime}(a, b, c)$. Then $a+b+c=$

10Three Dimensional Geometry

The equation of a line passing through origin with direction angles $\frac{2 \pi}{3}, \frac{\pi}{4}, \frac{\pi}{3}$ is

11Three Dimensional Geometry

Two lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect at a point. Then the value of ' $k$ ' is

12Three Dimensional Geometry

If $Q(1,0,1)$ is the image of the point $P(a, b, c)$ in the line $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}$ then $a+b+c$ is equal to :

13Three Dimensional Geometry

Shortest distance between the lines $\vec{r}=(8+3 \lambda) \hat{\imath}-(9+16 \lambda) \hat{\jmath}+(10+7 \lambda) \hat{k}$ and $\vec{r}=15 \hat{\imath}+29 \hat{\jmath}+5 \hat{k}+\mu(3 \hat{\imath}+8 \hat{\jmath}-5 \hat{k})$ is

14Three Dimensional Geometry

The length of the perpendicular from the point $P(1,-1,2)$ to the given line $\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z+2}{4}$ is

15Three Dimensional Geometry

The foot of the perpendicular from \((2,4,-1)\) to the line \(x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)\) is

16Three Dimensional Geometry

\(P\) is a point on the line segment joining the points \((3,2,-1)\) and \((6,2,-2)\). If \(x\) coordinate of \(\mathrm{P}\) is 5, then its \(y\) co-ordinate is

17Three Dimensional Geometry

The vector equation of two lines are
$$\begin{aligned} & \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \\ & \vec{r}=(s+1) \hat{\imath}+(2 s-1) \hat{\jmath}-(2 s+1) \hat{k} \end{aligned}$$
Then the shortest distance between t...

18Three Dimensional Geometry

The co-ordinate of the foot of the perpendicular from \(P(1,8,4)\) on the line joining \(R(0,-1,3)\) and \(Q(2,-3,-1)\) is

19Three Dimensional Geometry

The measure of the angle between the lines \(x=k+1, \quad y=2 k-1, \quad z=2 k+3, \quad k \in R \quad\) and \(\quad \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-1}{-2}\) is

20Three Dimensional Geometry

If the straight lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-t}\) and \(\frac{x-1}{t}=\frac{y-4}{2}=\frac{z-5}{1}\) are intersecting then \(t\) can have

21Three Dimensional Geometry

If the line \(\frac{1-x}{-3}=y=\frac{z+2}{2}\) is perpendicular to the line \(\frac{3 x-1}{2 b}=3-y=\frac{z-1}{a}\), then find the value of \(3 a+3 b\)

22Three Dimensional Geometry

A line makes the same angle \(\theta\) with each of the \(x\) and \(z\)-axes. If the angle \(\beta\), which it makes with the \(y\)-axis is such that \(\sin ^2 \beta=3 \sin ^2 \theta\), then \(\cos ^2 \theta\) equals

23Three Dimensional Geometry

The lines
\(\vec{r}=(2 \hat{\jmath}-3 \hat{k})+\lambda(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})\) and \(\vec{r}=(2 \hat{\imath}+6 \hat{\jmath}+3 \hat{k})+\mu(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})\) are

24Three Dimensional Geometry

If the direction ratios of two lines are given by \(3 l m-4 l n+m n=0\) and \(l+2 m+3 n=0\), then the angle between the lines is

25Three Dimensional Geometry

If the position vector of a point \(A\) is \(\vec{a}+2 \vec{b}\) and \(\vec{a}\) divides \(A B\) in the ratio \(2: 3\), then the position vector of \(B\) is

26Three Dimensional Geometry

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

27Three Dimensional Geometry

\(\mathrm{P} \text { is a point on the line segment joining the points }(3,2,-1) \text { and }(6,2,-2) \text {. If the } x \text { co ordinate of } \mathrm{P} \text { is } 5 \text {, then its } \mathrm{y} \text { coordinate is }\)

28Three Dimensional Geometry

The coordinates of the vertices of the triangle are \(A(-2,3,6), B(-4,4,9)\) and \(C(0,5,8)\). The direction cosines of the median \(\mathrm{BE}\) are

29Three Dimensional Geometry

If two lines \(L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\) and \(L_2: \frac{x-3}{1}=\frac{y-k}{2}=z\) intersect at a point, then \(2 k\) is equal to

30Three Dimensional Geometry

The lines \(\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}\) and \(\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}\) are perpendicular to each other, then \(a\) equals to

31Three Dimensional Geometry

The place \(x-2 y+z=0\) is parallel to the line

32Three Dimensional Geometry

The point of intersection of the lines \({{x - 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}\) and \({{x -5} \over 2} = {{y - 2} \over 1} = z\) is

33Three Dimensional Geometry

The angle between the lines \({{x + 4} \over 3} = {{y - 1} \over 5} = {{z + 3} \over 4}\) and \({{x + 1} \over 1} = {{y - 4} \over 1} = {{z - 5} \over 2}\) is

34Three Dimensional Geometry

The line \(\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}\) is parallel to the plane