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RD Sharma books are the best source of information for CBSE Maths students. It is a benchmark material for exam preparation. Many CBSE schools all over the country follow RD Sharma's book as they are informative and cover all concepts in detail.

RD Sharma Class 12th VSAQ is an exercise from the chapter ‘The Plane,’ containing 24 VSAQs. RD Sharma solutions Here students will learn about concepts like finding the equation of plane passing through points, equation of plane in scalar product form, angle, and vertices parallel and perpendicular to other planes. This exercise will help students learn critical concepts of vector algebra.

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The Plane exercise very short answer type question 1

Z = 5

Equation of the XY plane ⇒ Z = 0

Equation of the XY plane ⇒ Z = 0

Equation of the plane parallel to XOY plane ⇒Z=k …(i)

If Z = k Passing through (2, -3, 5) then 5 = k …(ii)

Equating (i) and (ii) ⇒ Z = 5

The Plane exercise very short answer type question 2

X = - 4

Equation of YZ plane ⇒ X = 0

plane parallel to YOZ plane and passing through (-4, 1, 0)

Equation of YZ plane ⇒ X = 0

Equation of the plane parallel to YOZ plane ⇒ X = k …(i)

If X=k Passing through (-4, 1, 0) then -4 = k …(ii)

Equating (i) and (ii) ⇒ X = -4

The Plane exercise very short answer type question 3

use formula

plane passing through (a, o, o), (o, b, o) and (o, o, c)

plane will cut x- axis at a

y- axis at b

z- axis at c

General eqn of plane

The Plane exercise very short answer type question 4

by + cz + d = 0

plane lie in yz plane.

plane parallel to x-axis

Let the general eqn of plane is ax + by + cz + d = 0 …(i)

This plane is parallel to x-axis.

It means that this plane will pass through

a.0 + b.y + c.z + d = 0

⇒ by + cz + d = 0

The Plane exercise very short answer type question 5

k = -8

If two vectors are perpendicular then their dot product is zero

Equation of first plane x - 2y + kz = 4 … (i)

Normal vector of plane (i) is

Equation of second plane 2x + 5y - z = 9 …(ii)

Normal vector of plane (ii) is

(i) and (ii) are perpendicular to each other

The Plane exercise very short answer type question 6

x- axis at 6, y- axis at -4, z-axis at 3

Intercept form of plane

Equation of plane 2x - 3y + 4z = 12

2x - 3y + 4z = 12

Plane intercept x- axis at 6

y- axis at -4

z- axis at 3

The Plane exercise very short answer type question 7

2 : 1

4x + 5y - 3z = 8 divides the line segment joining the points (-2, 1, 5) & (3, 3, 2)

Let the coordinate of A (-2, 1, 5) and B(3, 3, 2)

Let 4x + 5y - 3z = 8 …(i) divides the line segment AB at C in K : 1

C = internal section of AB

Co- ordinate of

Put the coordinate of C in (i)

Ratio K: 1 will be 2:1

The Plane exercise very short answer type question 8

parallel planes are 2x - y + 3z = 4 and 2x - y + 3z = 18

2x - y + 3z = 4

2x - y + 3z = 18

Distance =

The Plane exercise very short answer type question 9

Plane in normal form,

The Plane exercise very short answer type question 10

4 units

Point (0, 0, 0)

The Plane exercise very short answer type question 11

Plane passes through and parallel to & .

Normal vector will be ⊥ to & .

Putting in

The Plane exercise very short answer type question 12

Plane (i) parallel to

Normal vector of (i) ⊥ to be both

The Plane exercise very short answer type question 13

3x + 2y - z = 3

Plane parallel to 3x + 2y - z = 7 is 3x + 2y - z = λ

Plane passing through (2,-1,1) and ? to 3x + 2y - z = 7

3x + 2y - z = 7 ...(i)

∴ Eqn of parallel to (i)

3x + 2y - z = λ ...(ii)

(ii) Passes through (2,-1,1)

3(2) + 2(-1) - (1) = λ

λ = 3

∴ Eqn. (ii) Become 3x + 2y - z = 3

The Plane exercise very short answer type question 14

Equation of plane in scalar product form

Plane will pass through .

Normal of plane will be ⊥ to be both &

∴ General Eqn of the plane

The Plane exercise very short answer type question 15

Put (i) in(ii).

Putting the value of λ in eqn (i), we get

The Plane exercise very short answer type question 16

Use this formula if two planes are perpendicular a

So the vector normal to the plane as,

a

and

a

Since (i) and (ii) ⊥ to each other.

The Plane exercise very short answer type question 17

45°

So the vector normal to the plane (i) is

Cartesian equation of plane is

Since

The Plane exercise very short answer type question 18

2x + y - z = 5

2x + y - z = 5 .....(i)

Plane (i) cut x-axis at

The Plane exercise very short answer type question 19

3 units

2x - 3y + 6z + 21 = 0

2x - 3y + 6z + 21 = 0 ......(i)

Point of origin (0,0,0)

Distance of plane (i) from (0,0,0)

The Plane exercise very short answer type question 20

we will use vector equation of line as

Line passing through (1,-2,-3) and normal the plane

Position vector of point (1,-2,-3).

Given equation of plane

So the vector, normal to the plane is

∴Eqn. of line

Where λ is parameter.

The Plane exercise very short answer type question 21

we will use equation of plane as

Plane passing through (a,b,c) and parallel to plane

So the vector, normal to the plane is

∴Eqn. of plane to (i) is

Plane (ii) passing through (a,b,c)

Putting (iii) in (ii), we get

The Plane exercise very short answer type question 22

we will use equation of plane as

Normal vector of plane is

and distance from the origin =5 units

We know that

The Plane exercise very short answer type question 23

x + y + z = 15

Distance from the origin

Since the normal of plane equation inclined to co-ordinate axes

We know that

∴Equation of plane lx + my + nz = d, d = distance from origin

The Plane exercise very short answer type question 24

So the vector, normal to the plane is

So the vector, normal to the plane is

Angle between (i) & (ii)

RD Sharma Class 12th VSAQ material provided by Career360 is created to help students stay ahead and excel in their exams. The following are the benefits of these solutions:

**1. Exam-oriented**

RD Sharma Class 12th VSAQ solutions are prepared to provide answers for the RD Sharma book. As it follows the CBSE syllabus, students can directly refer to it to stay ahead of their classes and prepare for their exams. Moreover, as this material is updated to the latest version, students can benefit because it contains the newest questions.

**2. Easy to understand**

As RD Sharma Class 12th VSAQ material contains step-by-step solutions, it becomes easy to understand for students. This would help give a head start for students who are weak in maths. Furthermore, as Math is a simple subject that requires some practice, students can easily refer to this material to learn about the chapter and practice accordingly.

**3. Prepared by experts**

RD Sharma Class 12th VSAQ material is prepared by a group of subject experts with years of experience on CBSE question papers. There are different ways to solve a problem in maths, students can choose the best one that suits them through this material. Furthermore, all the steps and solutions provided in this book comply with the CBSE syllabus, so students don't have to worry about the correctness of the steps.

**4. Convenient**

RD Sharma Class 12 Chapter 28 VSAQ material is available on Career360’s website, and students can access these solutions using any device with an internet connection. This is an added benefit as students don't have to carry physical material everywhere and can study from any location, anytime. This paperless solution is the future of learning and is best for the preparation of students.

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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. Does this material cover all topics from the chapter?

Yes, this material is exam-oriented and covers all topics from the chapter. It is created to act as a guide for RD Sharma books.

2. Do I have to pay any hidden charges?

This material is available for free on the Career360 website and has no hidden costs. In addition, students can directly refer to their materials by searching their book names and exercise on the website.

3. Can I use this material on any device?

All this material requires is an internet connection. Thus, it can be accessed from any device, anywhere, through a browser.

4. Who can use this material?

RD Sharma Class 12 Solutions The Plane VSAQ is meant for CBSE students who find RD Sharma booms confusing and want to learn from simple material to understand the subject better.

5. Can I score good marks through these solutions?

RD Sharma Class 12 solutions Chapter 28 VSAQ will help students get an excellent Headstart for their exam preparation. Moreover, as it contains answers to the RD Sharma book, students can refer to it to quickly finish the exercises while getting a better understanding.

Sep 11, 2024

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