MEDIUM

JEE Main

IMPORTANT

Earn 100

If the plane $P$ passes through the intersection of two mutually perpendicular planes $2 x + k y - 5 z = 1$ and $3 k x - k y + z = 5, k < 3$ and intercepts a unit length on positive $x$ -axis, then the intercept made by the plane $P$ on the $y$ -axis is

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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 - 27 July 2022 Shift 1>Q 162

Let the line

\frac{x - 3}{7} = \frac{y - 2}{- 1} = \frac{z - 3}{- 4}

intersect the plane containing the lines

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

and

4 a x - y + 5 z - 7 a = 0 = 2 x - 5 y - z - 3, a \in ℝ

at the point

P (α, β, γ)

. Then the value of

α + β + γ

equals ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 July 2022 Shift 2>Q 163

If the length of the perpendicular drawn from the point

P (a, 4, 2), a > 0

on the line

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

2 \sqrt{6}

units and

Q (α_{1}, α_{2}, α_{3})

is the image of the point

P

in this line, then

a + \sum_{i = 1}^{3} α_{i}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 July 2022 Shift 2>Q 164

If the line of intersection of the planes

a x + b y = 3

and

a x + b y + c z = 0, a > 0

makes an angle

30 °

with the plane

y - z + 2 = 0

, then the direction cosines of the line are

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 July 2022 Shift 1>Q 165

The foot of the perpendicular from a point on the circle

x^{2} + y^{2} = 1, z = 0

to the plane

2 x + 3 y + z = 6

lies on which one of the following curves?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 28 July 2022 Shift 2>Q 166

Let the lines

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

and

\frac{x + 26}{- 2} = \frac{y + 18}{3} = \frac{z + 28}{λ}

be coplanar and

P

be the plane containing these two lines. 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 - 29 July 2022 Shift 1>Q 167

If the foot of the perpendicular from the point

A (- 1, 4, 3)

on the plane

P : 2 x + m y + n z = 4

, is

(- 2, \frac{7}{2}, \frac{3}{2})

, then the distance of the point

A

from the plane

P

, measured parallel to a line with direction ratios

3, - 1, - 4

, is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 29 July 2022 Shift 1>Q 168

Let a line with direction ratios

a, - 4 a, - 7

be perpendicular to the lines with direction ratios

3, - 1, 2 b

and

b, a, - 2

. If the point of intersection of the line

\frac{x + 1}{a^{2} + b^{2}} = \frac{y - 2}{a^{2} - b^{2}} = \frac{z}{1}

and the plane

x - y + z = 0

(α, β, γ)

, then

α + β + γ

is equal to ________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 29 July 2022 Shift 2>Q 169

Let

Q

be the foot of perpendicular drawn from the point

P (1, 2, 3)

to the plane

x + 2 y + z = 14

. If

R

is a point on the plane such that

∠ P R Q = 60 °

, then the area of

∆ P Q R

is equal to

If the plane P passes through the intersection of two mutually perpendicular planes 2x+ky-5z=1 and 3kx-ky+z=5,k<3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is

Important Questions on Three Dimensional Geometry

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If the plane $P$ passes through the intersection of two mutually perpendicular planes $2 x + k y - 5 z = 1$ and $3 k x - k y + z = 5, k < 3$ and intercepts a unit length on positive $x$ -axis, then the intercept made by the plane $P$ on the $y$ -axis is