Reflection of the line x - 1 - 1 = y - 2 3 = z - 4 1 in the plane x + y + z = 7 is

x - 1 - 3 = y - 2 1 = z - 4 - 1

x - 1 - 3 = y - 2 - 1 = z - 4 1

MEDIUM

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The $x$ -intercept of a plane $π$ passing through the point $(1, 1, 1)$ is $\frac{5}{2}$ and the perpendicular distance from the origin to the plane $π$ is $\frac{5}{7}$ . If the $y$ -intercept of the plane $π$ is negative and the $z$ -intercept is positive then its $y$ -intercept is

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Important Questions on Line and Plane

EASY

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

The distance of the point

(4, 2, 3)

from the plane

\vec{r} \cdot (6 \hat{i} + 2 \hat{j} - 9 \hat{k}) = 46

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Foot of the perpendicular drawn from the point

(1, 3, 4)

to the plane

2 x - y + z + 3 = 0

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

The distances of the point

(1, - 5, 9)

from the plane

x - y + z = 5

measured along a straight line

x = y = z

2 \sqrt{3} k

, then the value of

k

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

A perpendicular is drawn from a point on the line

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

to the plane

x + y + z = 3

such that the foot of the perpendicular

Q

also lies on the plane

x - y + z = 3

. Then the coordinates of

Q

are

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

The coordinates of the foot of the perpendicular drawn from the origin to plane

2 x - 3 y + 4 z - 6 = 0

, are

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

The mirror image of the point

(1, 2, 3)

in a plane is

(- \frac{7}{3}, - \frac{4}{3}, - \frac{1}{3}) .

Which of the following points lies on this plane?

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

The image of the point

(1, - 1, 1)

in the plane

x - 2 y + 3 z + 1 = 0

EASY

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Equations of planes parallel to the plane

x - 2 y + 2 z + 4 = 0

which are at a distance of one unit from the point

(1,2, 3)

are …..

MEDIUM

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

EASY

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

If the distance of points

2 \hat{i} + 3 \hat{j} + λ \hat{k}

from the plane

\vec{r} \cdot (3 \hat{i} + 2 \hat{j} + 6 \hat{k}) = 13

5

units then

λ =

EASY

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

If the sum of squares of distances of a point from the planes

x + y + z = 0, x - z = 0

and

x - 2 y + z = 0

p^{2}

then locus of the point is

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

A plane passing through the point

(3, 1, 1)

contains two lines whose direction ratios are

1, - 2, 2

and

2, 3, - 1

respectively. If this plane also passes through the point

(α, - 3, 5)

, then

α

is equal to

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Reflection of the line

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

in the plane

x + y + z = 7

EASY

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

A B

and

C D

are

2

line segments, where

A (2, 3, 0), B (6, 9, 0), C (- 6, - 9, 0)

and

D

is the image of point

A

about origin.

P

and

Q

are midpoint of

A B

and

C D

, respectively and

L

is the midpoint of

P Q

. Find the distance of

L

from the plane

3 x + 4 z + 25 = 0

EASY

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Find the distance (in units) of the point

(1, 2, 3)

from the plane

3 y + 4 z + 4 = 0

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Let

P

be a plane passing through the points

(2, 1, 0), (4, 1, 1)

and

(5, 0, 1)

and

R

be any point

(2, 1, 6)

.Then the image of

R

in the plane

P

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

Perpendiculars are drawn from points on the line

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

to the plane

x + y + z = 3

. The feet of perpendiculars lie on the line

HARD

Mathematics>Coordinate Geometry>Line and Plane>Equation of a Plane and Related Concepts

The perpendicular distance from the origin to the plane containing the two lines,

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

and

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

, is

The x-intercept of a plane π passing through the point 1,1,1 is 52 and the perpendicular distance from the origin to the plane π is 57. If the y-intercept of the plane π is negative and the z-intercept is positive then its y-intercept is

Important Questions on Line and Plane

Learn and Prepare for any exam you want !

The $x$ -intercept of a plane $π$ passing through the point $(1, 1, 1)$ is $\frac{5}{2}$ and the perpendicular distance from the origin to the plane $π$ is $\frac{5}{7}$ . If the $y$ -intercept of the plane $π$ is negative and the $z$ -intercept is positive then its $y$ -intercept is