EASY

JEE Main

IMPORTANT

Earn 100

If the mirror image of the point $(2, 4, 7)$ in the plane $3 x - y + 4 z = 2$ is $(a, b, c)$ , then $2 a + b + 2 c$ is equal to

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Important Questions on Three Dimensional Geometry

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 29 June 2022 Shift 1>Q 149

Let

d

be the distance between the foot of perpendiculars of the points

P (1, 2 - 1)

and

Q (2, - 1, 3)

on the plane

- x + y + z = 1

. Then

d^{2}

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 29 June 2022 Shift 1>Q 150

Let

P_{1} : \vec{r} \cdot (2 \hat{i} + \hat{j} - 3 \hat{k}) = 4

be a plane. Let

P_{2}

be another plane which passes through the points

(2, - 3, 2) (2, - 2, - 3)

and

(1, - 4, 2)

. If the direction ratios of the line of intersection of

P_{1}

and

P_{2}

16

α, β

, then the value of

α + β

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 29 June 2022 Shift 2>Q 151

Let

\frac{x - 2}{3} = \frac{y + 1}{- 2} = \frac{z + 3}{- 1}

lie on the plane

p x - q y + z = 5

, for some

p, q \in R

. The shortest distance of the plane from the origin is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 29 June 2022 Shift 2>Q 152

Let

Q

be the mirror image of the point

P (1, 2, 1)

with respect to the plane

x + 2 y + 2 z = 16

. Let

T

be a plane passing through the point

Q

and contains the line

\vec{r} = - \hat{k} + λ (\hat{i} + \hat{j} + 2 \hat{k}), λ \in R

. Then, which of the following points lies on

T

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 25 July 2022 Shift 1>Q 153

Let

P

be the plane containing the straight line

\frac{x - 3}{9} = \frac{y + 4}{- 1} = \frac{z - 7}{- 5}

and perpendicular to the plane containing the straight lines

\frac{x}{2} = \frac{y}{3} = \frac{z}{5}

and

\frac{x}{3} = \frac{y}{7} = \frac{z}{8}

. If

d

is the distance of

P

from the point

(2, - 5, 11)

, then

d^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 25 July 2022 Shift 1>Q 154

The line of shortest distance between the lines

\frac{x - 2}{0} = \frac{y - 1}{1} = \frac{z}{1}

and

\frac{x - 3}{2} = \frac{y - 5}{2} = \frac{z - 1}{1}

makes an angle of

\sin^{- 1} (\sqrt{\frac{2}{27}})

with the plane

P : a x - y - z = 0, (a > 0)

. If the image of the point

(1, 1, - 5)

in the plane

P

(α, β, γ)

, then

α + β - γ

is equal to _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 25 July 2022 Shift 2>Q 155

A plane

E

is perpendicular to the two planes

2 x - 2 y + z = 0

and

x - y + 2 z = 4

, and passes through the point

P (1, - 1, 1)

. If the distance of the plane

E

from the point

Q (a, a, 2)

3 \sqrt{2}

, then

{(P Q)}^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 26 July 2022 Shift 1>Q 156

If the system of linear equations.

$8 x + y + 4 z = - 2$

$x + y + z = 0$

$λ x - 3 y = μ$

has infinitely many solutions, then the distance of the point $(λ, μ, - \frac{1}{2})$ from the plane $8 x + y + 4 z + 2 = 0$ is:

If the mirror image of the point 2,4,7 in the plane 3x-y+4z=2 is a,b,c, then 2a+b+2c is equal to

Important Questions on Three Dimensional Geometry

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If the mirror image of the point $(2, 4, 7)$ in the plane $3 x - y + 4 z = 2$ is $(a, b, c)$ , then $2 a + b + 2 c$ is equal to