HARD

JEE Main

IMPORTANT

Earn 100

Let the plane $2 x + 3 y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3 y + 5 z = 8$ . If the mirror image of the point $(2, - \frac{1}{2}, 2)$ in the rotated plane is $B (a, b, c)$ , then

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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 - 27 June 2022 Shift 1>Q 140

If two straight lines whose direction cosines are given by the relations

l + m - n = 0, 3 l^{2} + m^{2} + c n l = 0

are parallel, then the positive value of

c

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 June 2022 Shift 1>Q 141

Let the mirror image of the point

(a, b, c)

with respect to the plane

3 x - 4 y + 12 z + 19 = 0

(a - 6, β, γ)

. If

a + b + c = 5

, then

7 β - 9 γ

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 June 2022 Shift 2>Q 142

Let the foot of the perpendicular from the point

(1, 2, 4)

on the line

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

P

. Then the distance of

P

from the plane

3 x + 4 y + 12 z + 23 = 0

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 June 2022 Shift 1>Q 143

If two distinct point

Q, R

lie on the line of intersection of the planes

- x + 2 y - z = 0

and

3 x - 5 y + 2 z = 0

and

P Q = P R = \sqrt{18}

where the point

P

(1, - 2, 3)

, then the area of the triangle

P Q R

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 June 2022 Shift 1>Q 144

The acute angle between the planes

P_{1}

and

P_{2}

, when

P_{1}

and

P_{2}

are the planes passing through the intersection of the planes

5 x + 8 y + 13 z - 29 = 0

and

8 x - 7 y + z - 20 = 0

and the points

(2, 1, 3)

and

(0, 1, 2)

, respectively, is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 June 2022 Shift 1>Q 145

Let the plane

P : \vec{r} \cdot \vec{a} = d

contain the line of intersection of two planes

\vec{r} \cdot (\hat{i} + 3 \hat{j} - \hat{k}) = 6

and

\vec{r} \cdot (- 6 \hat{i} + 5 \hat{j} - \hat{k}) = 7

. If the plane

P

passes through the point

(2, 3, \frac{1}{2})

, then the value of

\frac{{|13 \vec{a}|}^{2}}{d^{2}}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 June 2022 Shift 2>Q 146

Let the plane $a x + b y + c z = d$ pass through $(2, 3, - 5)$ and is perpendicular to the planes $2 x + y - 5 z = 10$ and $3 x + 5 y - 7 z = 12$

If $a, b, c, d$ are integers $d > 0$ and $g c d (|a|, |b|, |c|, d) = 1$ then the value of $a + 7 b + c + 20 d$ is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 June 2022 Shift 2>Q 147

Let the image of the point

P (1, 2, 3)

in the line

L : \frac{x - 6}{3} = \frac{y - 1}{2} = \frac{z - 2}{3}

Q

. let

R (α, β, γ)

be a point that divides internally the line segment

P Q

in the ratio

1 : 3

. Then the value of

22 (α + β + γ)

is equal to

Let the plane 2x+3y+z+20=0 be rotated through a right angle about its line of intersection with the plane x-3y+5z=8. If the mirror image of the point 2,-12,2 in the rotated plane is Ba,b,c, then

Important Questions on Three Dimensional Geometry

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Let the plane $2 x + 3 y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3 y + 5 z = 8$ . If the mirror image of the point $(2, - \frac{1}{2}, 2)$ in the rotated plane is $B (a, b, c)$ , then