EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 31 January 2023 Shift 2>Q 197

EASY

JEE Main

IMPORTANT

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Let $P$ be the plane, passing through the point $(1, - 1, - 5)$ and perpendicular to the line joining the points $(4, 1, - 3)$ and $(2, 4, 3)$ . Then the distance of $P$ from the point $(3, - 2, 2)$ is

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Important Questions on Three Dimensional Geometry

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 31 January 2023 Shift 2>Q 198

Let the plane

P : 8 x + α_{1} y + α_{2} z + 12 = 0

be parallel to the line

L : \frac{x + 2}{2} = \frac{y - 3}{3} = \frac{z + 4}{5}

. If the intercept of

P

on the

y

-axis is

1

, then the distance between

P

and

L

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 1 February 2023 Shift 1>Q 199

The shortest distance between the lines

\frac{x - 5}{1} = \frac{y - 2}{2} = \frac{z - 4}{- 3}

and

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

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 1 February 2023 Shift 1>Q 200

Let the image of the point

P (2, - 1, 3)

in the plane

x + 2 y - z = 0

be

Q

. Then the distance of the plane

3 x + 2 y + z + 29 = 0

from the point

Q

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 1 February 2023 Shift 2>Q 201

Let the plane

P

pass through the intersection of the planes

2 x + 3 y - z = 2

and

x + 2 y + 3 z = 6

, and be perpendicular to the plane

2 x + y - z + 1 = 0

. If

d

is the distance of

P

from the point

(- 7, 1, 1)

, then

d^{2}

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 1 February 2023 Shift 2>Q 202

Let

α x + β y + γ z = 1

be the equation of a plane passing through the point

(3, - 2, 5)

and perpendicular to the line joining the points

(1, 2, 3)

and

(- 2, 3, 5)

. Then the value of

α β y

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 1 February 2023 Shift 2>Q 203

The point of intersection

C

of the plane

8 x + y + 2 z = 0

and the line joining the points

A (- 3, - 6, 1)

and

B (2, 4, - 3)

divides the line segment

A B

internally in the ratio

k : 1

. If

a, b, c

(| a |, | b |, | c |

are coprime) are the direction ratios of the perpendicular from the point

C

on the line

\frac{1 - x}{1} = \frac{y + 4}{2} = \frac{z + 2}{3}

, then

|a + b + c|

is equal to _____ .