The equation of the plane passing through the line of intersection of the planes r → · ( i ^ + j ^ + k ^ ) = 1 and r → · ( 2 i ^ + 3 j ^ - k ^ ) + 4 = 0 and parallel to the x -axis, is

r → · ( j ^ - 3 k ^ ) + 6 = 0

r → · ( i ^ + 3 k ^ ) + 6 = 0

r → · ( i ^ - 3 k ^ ) + 6 = 0

r → · ( j ^ - 3 k ^ ) - 6 = 0

HARD

JEE Main

IMPORTANT

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Let the line $L$ be the projection of the line $\frac{x - 1}{2} = \frac{y - 3}{1} = \frac{z - 4}{2}$ in the plane $x - 2 y - z = 3$ . If $d$ is the distance of the point $(0, 0, 6)$ from $L$ , then $d^{2}$ is equal to

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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 August 2021 Shift 2>Q 3

Let

P

be the plane passing through the point

(1, 2, 3)

and the line of intersection of the planes

\vec{r} \cdot (\hat{i} + \hat{j} + 4 \hat{k}) = 16 & \vec{r} \cdot (- \hat{i} + \hat{j} + \hat{k}) = 6

. Then which of the following points does NOT lie on

P

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 26 August 2021 Shift 2>Q 4

A hall has a square floor of dimension $10 m \times 10 m$ (see the figure) and vertical walls. If the angle $G P H$ between the diagonals $A G$ and $B H$ is $\cos^{- 1} \frac{1}{5},$ then the height of the hall (in meters) is:

Question Image

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 26 August 2021 Shift 2>Q 5

Let

Q

be the foot of the perpendicular from the point

P (7, - 2, 13)

on the plane containing the lines

\frac{x + 1}{6} = \frac{y - 1}{7} = \frac{z - 3}{8}

and

\frac{x - 1}{3} = \frac{y - 2}{5} = \frac{z - 3}{7}

Then

(P Q)^{2},

is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 August 2021 Shift 1>Q 6

The distance of the point

(1, - 2, 3)

from the plane

x - y + z = 5

measured parallel to a line, whose direction ratios are

2, 3, - 6

, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 August 2021 Shift 1>Q 7

Equation of a plane at a distance

\sqrt{\frac{2}{21}}

units from the origin, which contains the line of intersection of the planes

x - y - z - 1 = 0

and

2 x + y - 3 z + 4 = 0,

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 August 2021 Shift 2>Q 8

The equation of the plane passing through the line of intersection of the planes

\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1

and

\vec{r} \cdot (2 \hat{i} + 3 \hat{j} - \hat{k}) + 4 = 0

and parallel to the

x

-axis, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 August 2021 Shift 2>Q 9

The angle between the straight lines, whose direction cosines

l, m, n

are given by the equations

2 l + 2 m - n = 0

and

m n + n l + lm = 0

, is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 August 2021 Shift 2>Q 10

Let

S

be the mirror image of the point

Q (1, 3, 4)

with respect to the plane

2 x - y + z + 3 = 0

and let

R (3, 5, γ)

be a point of this plane. Then the square of the length of the line segment

S R

Let the line L be the projection of the line x-12=y-31=z-42 in the plane x-2y-z=3. If d is the distance of the point (0,0,6) from L, then d2 is equal to

Important Questions on Three Dimensional Geometry

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Let the line $L$ be the projection of the line $\frac{x - 1}{2} = \frac{y - 3}{1} = \frac{z - 4}{2}$ in the plane $x - 2 y - z = 3$ . If $d$ is the distance of the point $(0, 0, 6)$ from $L$ , then $d^{2}$ is equal to