Let P be the plane passing through the intersection of the planes r → · i ^ + 3 j ^ - k ^ = 5 and r → · 2 i ^ - j ^ + k ^ = 3 , and the point 2 , 1 , - 2 . Let the position vectors of the points X and Y be i ^ - 2 j ^ + 4 k ^ and 5 i ^ - j ^ + 2 k ^ respectively. Then the points

X and Y are on the opposite sides of P

X and X + Y are on the same side of P

Y and Y - X are on the opposite sides of P

X + Y and X - Y are on the same side of P

Let P be the plane passing through the intersection of the planes r → · i ^ + 3 j ^ - k ^ = 5 and r → · 2 i ^ - j ^ + k ^ = 3 , and the point 2 , 1 , - 2 . Let the position vectors of the points X and Y be i ^ - 2 j ^ + 4 k ^ and 5 i ^ - j ^ + 2 k ^ respectively. Then the points

X and Y are on the opposite sides of P

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Let $P$ be the plane passing through the intersection of the planes $\vec{r} \cdot (\hat{i} + 3 \hat{j} - \hat{k}) = 5$ and $\vec{r} \cdot (2 \hat{i} - \hat{j} + \hat{k}) = 3$ , and the point $(2, 1, - 2)$ . Let the position vectors of the points $X$ and $Y$ be $\hat{i} - 2 \hat{j} + 4 \hat{k}$ and $5 \hat{i} - \hat{j} + 2 \hat{k}$ respectively. Then the points

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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 - 26 June 2022 Shift 2>Q 136

If the plane

2 x + y - 5 z = 0

is rotated about its line of intersection with the plane

3 x - y + 4 z - 7 = 0

by an angle of

\frac{π}{2}

, then the plane after the rotation passes through the point

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 26 June 2022 Shift 2>Q 137

If the lines

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

and

\vec{r} = (α \hat{i} - \hat{j}) + μ (2 \hat{i} - 3 \hat{k})

are co-planar, the the distance of the plane containing these two lines from the point

(α, 0, 0)

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 26 June 2022 Shift 1>Q 138

If the two lines

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

and

l_{2} : \frac{x - 1}{1} = \frac{2 y + 3}{α} = \frac{z + 5}{2}

are perpendicular, then an angle between the lines

l_{2}

and

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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 26 June 2022 Shift 1>Q 139

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

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

Let P be the plane passing through the intersection of the planes r→·i^+3j^-k^=5 and r→·2i^-j^+k^=3, and the point 2,1,-2. Let the position vectors of the points X and Y be i^-2j^+4k^ and 5i^-j^+2k^ respectively. Then the points

Important Questions on Three Dimensional Geometry

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