Three Dimensional Geometry · Mathematics · COMEDK

Start Practice

MCQ (Single Correct Answer)

1
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 $a+b+c=$
COMEDK 2025 Evening Shift
2
The equation of a line passing through origin with direction angles $\frac{2 \pi}{3}, \frac{\pi}{4}, \frac{\pi}{3}$ is
COMEDK 2025 Evening Shift
3
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
COMEDK 2025 Evening Shift
4
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
COMEDK 2025 Afternoon Shift
5
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 :
COMEDK 2025 Afternoon Shift
6
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
COMEDK 2025 Afternoon Shift
7
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
COMEDK 2025 Morning Shift
8
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 $\frac{\pi}{2}$
COMEDK 2025 Morning Shift
9

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

COMEDK 2024 Evening Shift
10

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

COMEDK 2024 Evening Shift
11

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

COMEDK 2024 Evening Shift
12

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 $$3 a+3 b$$

COMEDK 2024 Afternoon Shift
13

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

COMEDK 2024 Afternoon Shift
14

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

COMEDK 2024 Afternoon Shift
15

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

COMEDK 2024 Morning Shift
16

$$P$$ 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

COMEDK 2024 Morning Shift
17

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 them is

COMEDK 2024 Morning Shift
18

The place $$x-2 y+z=0$$ is parallel to the line

COMEDK 2023 Morning Shift
19

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

COMEDK 2023 Morning Shift
20

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

COMEDK 2023 Morning Shift
21

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

COMEDK 2023 Evening Shift
22

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

COMEDK 2023 Evening Shift
23

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

COMEDK 2023 Evening Shift
24

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

COMEDK 2023 Evening Shift
25

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

COMEDK 2023 Evening Shift
26

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

COMEDK 2022
27

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

COMEDK 2022
28

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

COMEDK 2022
29

The line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ is parallel to the plane

COMEDK 2021
30

The equation of a plane passing through the line of intersection of the planes $$x+2y+3z=2,x-y+z=3$$ and at a distance $$\frac{2}{\sqrt3}$$ from the point $$(3,1,-1)$$ is

COMEDK 2021
31

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is

COMEDK 2021
32

The point of intersection of the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$ and $${{x - 4} \over 5} = {{y - 1} \over 2} = z$$ is

COMEDK 2021
33

A vector perpendicular to the plane containing the points $$A(1, - 1,2),B(2,0, - 1),C(0,2,1)$$ is

COMEDK 2020
EXAM MAP