Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 3

EASY

JEE Advanced

IMPORTANT

Earn 100

If $θ$ is the angle between the planes $2 x - y + z - 4 = 0$ and $x - 2 y + z + 2 = 0$ , then $\cos θ$ is equal to

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Important Questions on Three Dimensional Geometry

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 4

Distance between two parallel planes

4 x + 2 y + 4 z + 5 = 0

and

2 x + y + 2 z - 8 = 0

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 6

If

(2, - 1, 3)

is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 7

The equation of the plane passing through the points

(0, 1, 2)

and

(- 1, 0, 3)

and perpendicular to the plane

2 x + 3 y + z = 5

, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 8

The reflection of the plane

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

in the plane

x - y + z - 3 = 0

is the plane

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 9

The image of the point

(5, 4, 6)

in the plane

x + y + 2 z - 15 = 0

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.3>Q 10

A variable plane

\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1

at a unit distance from origin cuts the coordinate axes at

A, B

and

C .

If centroid

(x, y, z)

satisfies the equation

\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = k,

then the value of

k

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.4>Q 1

Angle between the line

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

and the plane

x - y + z = 0,

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 14 - Three Dimensional Geometry>Work Book Exercise 14.4>Q 2

If the plane

2 x - y + z = 0

is parallel to the line

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

then the value of

α

is