Three Dimensional Geometry · Mathematics · KCET

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MCQ (Single Correct Answer)

1

If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, where $\theta$ is acute, then the value of $\theta$ is

KCET 2025
2

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is

KCET 2025
3
The distance of the point $\mathrm{P}(-3,4,5)$ from yz plane is
KCET 2025
4

If lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are mutually perpendicular, then $k$ is equal to

KCET 2024
5

The distance between the two planes $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is

KCET 2024
6

The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5}$ are the plane $2 x-2 y+z=5$ is

KCET 2024
7

The equation $x y=0$ in three-dimensional space represents

KCET 2024
8

The plane containing the point $(3,2,0)$ and the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is

KCET 2024
9

If a line makes an angle of $$\frac{\pi}{3}$$ with each $$X$$ and $$Y$$ axis, then the acute angle made by $$\mathrm{Z}$$-axis is

KCET 2023
10

The length of perpendicular drawn from the point $$(3,-1,11)$$ to the line $$\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$ is

KCET 2023
11

The equation of the plane through the points $$(2,1,0),(3,2,-2)$$ and $$(3,1,7)$$ is

KCET 2023
12

The point of intersection of the line $$x+1=\frac{y+3}{3}=\frac{-z+2}{2}$$ with the plane $$3 x+4 y+5 z=10$$ is

KCET 2023
13

If $$(2,3,-1)$$ is the foot of the perpendicular from $$(4,2,1)$$ to a plane, then the equation of the plane is

KCET 2023
14

The octant in which the point (2, $$-$$4, $$-7$$) lies is

KCET 2022
15

The coordinates of foot of the perpendicular drawn from the origin to the plane $$2 x-3 y+4 z=29$$ are

KCET 2022
16

The angle between the pair of lines $$\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$$ and $$\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}$$ is

KCET 2022
17

The distance of the point whose position vector is $$(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})$$ from the plane $$\mathbf{r} \cdot(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=4$$ is

KCET 2022
18

The equation of the line joining the points $$(-3,4,11)$$ and $$(1,-2,7)$$ is

KCET 2021
19

The angle between the lines whose direction cosines are $$\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$$ and $$\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$$

KCET 2021
20

If a plane meets the coordinate axes at $$A, B$$ and $$C$$ in such a way that the centroid of $$\triangle A B C$$ is at the point $$(1,2,3)$$, then the equation of the plane is

KCET 2021
21

The area of the quadrilateral $$A B C D$$ when $$A(0,4,1), B(2,3,-1), C(4,5,0)$$ and $$D(2,6,2)$$ is equal to

KCET 2021
22

The mid points of the sides of triangle are $$(1,5,-1)(0,4,-2)$$ and $$(2,3,4)$$ then centroid of the triangle

KCET 2021
23

The point $$(1,-3,4)$$ lies in the octant

KCET 2020
24

The distance of the point $$(1,2,-4)$$ from the line $$\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}$$ is

KCET 2020
25

The sine of the angle between the straight line $$\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}$$ and the plane $$2 x-2 y+z=5$$ is

KCET 2020
26

If a line makes an angle of with each of $$X$$ and $$Y$$-axis, then the acute angle made by Z-axis is

KCET 2020
27

Foot of the perpendicular drawn from the point $$(1,3,4)$$ to the plane $$2 x-y+z+3=0$$ is

KCET 2019
28

Acute angel between the line $$\frac{(x-5)}{2}=\frac{y+1}{-1}=\frac{z+4}{1}$$ and the plane $$3 x-4 y-z+5=0$$ is

KCET 2019
29

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

KCET 2019
30

$$X Y$$ plane divides the line joining the points $$A(2,3,-5)$$ and $$B(-1,-2,-3)$$ in the ratio

KCET 2019
31
The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is
KCET 2018
32
The angle between the lines $2 x=3 y=-z$ and $6 x=-y=-4 z$ is
KCET 2018
33
The value of $k$ such that the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies on the plane $2 x-4 y+z=7$ is
KCET 2018
34
The locus represented by $x y+y z=0$ is
KCET 2018
35
The plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1}(\alpha)$ with $X$-axis, the value of $\alpha$ is equal to
KCET 2017
36
The perpendicular distance of the point $P(6,7,8)$ from $X Y$-plane is
KCET 2017
37
Reflexion of the point $(\alpha, \beta, \gamma)$ in $X Y$-plane is
KCET 2017
38
The distance of the point $(-2,4,-5)$ from the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is
KCET 2017
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