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RD Sharma books are the best books with regards to planning for board exams. However, board exams have consistently been viewed as a fabrication for some students. RD Sharma solutions In any case, when they allude to this book alongside Rd Sharma Class 12th Exercise FBQ solutions, they think that it is simpler to back out with a great deal of pressure and comprehend the idea in a vastly improved manner. This specific exercise has 20 inquiries from the general chapter. Rd Sharma Class 12th Exercise FBQ incorporates Equation of the plane containing two lines, Equation of the plane in scalar item structure, Reflection of point, Vector and Cartesian structure, condition of the plane in standard form, Shortest distance between two lines, and distance between the plane.

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The Plane exercise fill in the blank question 1

10

Use vector dot product

x + 2y - 2z = d, d>0

Perpendicular distance of the plane ax +by + cz + d = 0

Equation of plane parallel to x + 2y - 2z = d is

x + 2y -2z - d = 0 …………………………(1)

Perpendicular distance from (1,-2,1) is

The Plane exercise fill in the blank question 2

Two perpendicular plane equals 0

3x - 6y - 2z = 7 and 2x + y - λz = 5

The equations of planes are

3x - 6y - 2z -7 =0

and 2x + y - kz - 5 = 0

Since two planes are perpendicular to each other

∴(3)(2) + (-6)(1) + (-2) (-k) = 0 ? a

∴6 - 6 + 2k = 0 2k = 0

k = 0

The Plane exercise fill in the blank question 3

2X + 3Y - Y2 + 4 = 0

Equation of parallel to2x + 3y - y2 = 0 is given by

2x + 3y - y2 + λ = 0

Also It passes through (1,2,3)

? 2(1) + 3(2) - 4(3) + λ = 0 ? λ = 4

∴ required plane is 2x + 3y - y2 + 4 = 0

The Plane exercise fill in the blank question 4

Use bracket method

(1,2,3) and normal to the plane 2x - 3y + 6z = 11

Let the equation be

? we will get normal equation

? 2x - 3y + 6z = 11

The Plane exercise fill in the blank question 5

2x + 3y - 4k = 24 on the coordinate is 8

sum of intercepts

=2 + 3 - 4k = 24

The Plane exercise fill in the blank question 6

Solve using fraction method.

The Plane exercise fill in the blank question 7

Let the points a,b,c and try to get the equation

Let the point be (a,b,c)

The plane meets the coordinates are at

So, the plane cuts x- axis at (3a,0,0) , so, x- intercept = 3a

The plane cuts z- axis at (0,0,3c)?z- intercept =3c

The plane cuts y-axis at (0,3b,0)?y- intercept =3b

? all one getting the equation

∴ the point will be (a,b,c)

The Plane exercise fill in the blank question 8

ax + by + cz = a2 + b2 + c2

Firs find the co-ordinates

p(a,b,c) perpendicular to op

The coordinates of the points

It is known that the equation of the plane passing through the point (x,y,z) is

a(x - x

∴ the required equation will be

a(x - a) + b(y - b) + c(z - c) = 0

ax - a

ax + by + cz = a

The Plane exercise fill in the blank question 9

(2,2,2)

Sum of the reciprocals of its intercepts on the coordinates axis is 1/2

Let the equation of the variable plane be

The intercepts on the coordinate axes are a,b,c

Let the sum of reciprocals of intercept in constant =λ

Therefore,

lies on the plane (1)

Hence, the variable plane (1) always passes through

the fixed point

The Plane exercise fill in the blank question 10

x + αy +2 = 5

Given equation of plane

Comparing above equation with equation of plane in intercept from

So coordinates of points A,B,C?A(5,0,0),B(0,5,0),C(0,0,5)

Let circumentre D(x,y,z)

AD=BD=CD ? taking AD=BD

On squaring both sides

(x - 5)

∴ from equation (1) ,x,y can be x=1, y=1

∴ α=1 (also)(by solving)

The Plane exercise fill in the blank question 11

-4

Use vector dot product

is parallel to the plane 2x - y + z = 3

The Plane exercise fill in the blank question 12

The line is

The direction radius of the line are(3,-5,2)

As the line lies in the plane x + 3y - αz + 7 = 0

We have

The Plane exercise Fill in the blank question 13

Use direction ratios

Let the given line is

Direction ratios are λ,1,-4

And the given plane 2x+ 2y - 8z = -5

Its direction ratios are 2,2,-4

And the given line and plane are perpendicular, then

λ(1) + 1(1) + (-4)(-8) = 0

2λ + 2 + 16=0

λ = -9

The Plane exercise Fill in the blank question 14

6x + 4y + 3z = 12 is the required equation of plane

Equation of the plane that cut the coordinate axes =1

(2,0,0) , (0,3,0) and (0,0,4)

We know that, equation of the plane that cut the coordinate axes at

(2,0,0) , (0,3,0) and (0,0,4) is

Hence, the equation of plane passes through the points (2,0,0) , (0,3,0) and (0,0,4)

is

= 6x + 4y + 3z = 12

The Plane exercise fill in the blank question 15

x + y + z = 2 is the required Cartesian product

Use vector product

We have,

The Plane exercise Fill in the blank question 16

are the intercepts made by the plane

Convert the given equation into intercept form

First let’s convert the given equation to intercept form i.e

Where a,b,c are x,y nad z intercepts respectively

Given,

2x - 3y + 5z + 4 = 0

⇒ -2x + 3y - 5z = 4

Dividing by 4 both sides

On comparing we have intercepts as

The Plane exercise Fill in the blank question 17

is the angle between the line and the plane

Line

Is parallel to the vector

Normal to the plane is

Let is the angle between line and plane

Then,

The Plane exercise Fill in the blank question 18

is the required equation of plane.

Use figure to solve the equation

(5,-3,-2)

From the figure normal to the plane is

Plane passing through the point P(5,-3,-2)

Equation of plane is

In vector form

The Plane exercise Fill in the blank question 19

Let

The Plane exercise Fill in the blank question 20

x - 3z = 10 is the required Cartesian equation

use direction cosine formula.

P(1,0,-3)

Assume direction cosine of the normal (a,b,c)

Equation of plane passing through (x,y,z)

Point P(1,0,-3)

Direction cosine of normal

(a,b,c) = (1 - 0, 0 - 0, -3 - 0)

(a,b,c) = (1,0,-3)

Equation of the plane

[(x - 1)+ 0 (y - 0) - 3 (2- (-3))]=0

x - 3z = 10

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- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. How are two planes related to each other?

In a three-dimensional space, two planes can be related in three ways.

1. They can run parallel to one another.

2. They can be the same.

3. They can cross each other.

2. What are the properties of planes?

In a three-dimensional space, if there are two different planes, they are either parallel to each other or intersect in a line.

A line can be parallel to a plane, intersect it at a single point, or exist within the plane.

If two different lines are perpendicular to each other on the same plane, they must be parallel to one another.

If two different planes are perpendicular to a common line, they must be parallel to one another.

3. What exactly is a Plane Figure?

A plane figure is any geometric figure with no thickness.

4. Is it enough to study from RD Sharma Class 12 solutions from an exam point of view?

Rd Sharma Class 12th Exercise FBQ are compiled in a step-by-step manner in simple language for students' ease of comprehension. Referring to these solutions while solving can help students improve their conceptual knowledge.

5. What is the best website for studying RD Sharma Solutions for Class 12 Maths?

On the Career360 website, you can find Rd Sharma Class 12th Exercise FBQ solutions, as well as step-by-step answers to all of the questions in the RD Sharma textbook. As a result, in order to understand the important topics, students in Class 12 should learn all of the concepts covered in the syllabus.

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