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JEE Main

IMPORTANT

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Let the foot of perpendicular from a point $P (1, 2, - 1)$ to the straight line $L : \frac{x}{1} = \frac{y}{0} = \frac{z}{- 1}$ be $N$ . Let a line be drawn from $P$ parallel to the plane $x + y + 2 z = 0$ which meets $L$ at point $Q$ . If $α$ is the acute angle between the lines $P N$ and $P Q$ , then $\cos α$ is equal to .

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Important Questions on Three Dimensional Geometry

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 25 July 2021 Shift 2>Q 23

If the lines

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

and

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

are co-planar, then the value of

k

is _______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 July 2021 Shift 1>Q 24

Let the plane passing through the point

(- 1, 0, - 2)

and perpendicular to each of the planes

2 x + y - z = 2

and

x - y - z = 3

a x + b y + c z + 8 = 0 .

Then the value of

a + b + c

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 July 2021 Shift 1>Q 25

Let a plane

P

pass through the point

(3, 7, - 7)

and contain the line,

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

If distance of the plane

P

from the origin is

d,

then

d^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 27 July 2021 Shift 2>Q 26

For real numbers

α

and

β \neq 0,

if the point of intersection of the straight lines

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

and

\frac{x - 4}{β} = \frac{y - 6}{3} = \frac{z - 7}{3}

lies on the plane

x + 2 y - z = 8,

then

α - β

is equal to :

MEDIUM

JEE Main

IMPORTANT

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

The distance of the point

P (3, 4, 4)

from the point of intersection of the line joining the points

Q (3, - 4, - 5)

and

R (2, - 3, 1)

and the plane

2 x + y + z = 7,

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main 16 March 2021 Shift 1>Q 28

If for

a > 0

, the feet of perpendiculars from the points

A (a, - 2 a, 3)

and

B (0, 4, 5)

on the plane

l x + m y + n z = 0

are points

C (0, - a, - 1)

and

D

respectively, then the length of line segment

C D

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main 16 March 2021 Shift 1>Q 29

Let the position vectors of two points

P

and

Q

3 \hat{i} - \hat{j} + 2 \hat{k}

and

\hat{i} + 2 \hat{j} - 4 \hat{k}

, respectively. Let

R

and

S

be two points such that the direction ratios of lines

P R

and

Q S

are

(4, - 1, 2)

and

(- 2, 1, - 2)

, respectively. Let lines

P R

and

Q S

intersect at

T

. If the vector

\vec{T A}

is perpendicular to both

\vec{P R}

and

\vec{Q S}

and the length of vector

\vec{T A}

\sqrt{5}

units, then the modulus of a position vector of

A

is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main 16 March 2021 Shift 1>Q 30

Let

P

be a plane

l x + m y + n z = 0

containing the line,

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

. If plane

P

divides the line segment

A B

joining points

A (- 3, - 6, 1)

and

B (2, 4, - 3)

in ratio

k : 1

then the value of

k

is equal to :

Let the foot of perpendicular from a point P(1,2,-1) to the straight line L:x1=y0=z-1 be N. Let a line be drawn from P parallel to the plane x+y+2z=0 which meets L at point Q. If α is the acute angle between the lines PN and PQ, then cosα is equal to .

Important Questions on Three Dimensional Geometry

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