Vectors and 3D Geometry for JEE (Advanced), 3rd edition 9353503817, 9789353503819

Citation preview

Contents

vii

Preface 1.

Introduction to 3D Geometry Introduction to 3D Coordinate System

1.1

Understanding Coordinates of Point in 3D System

1.2

Direction Angles and Direction Cosines

1.5

Plane Perpendicular to One of the Three Axes

1.7

Line Parallel to One of the Three Axes

1.8

Concept Application Exercise 1.1 Distance Formula Distance between Two Points Lying on the Sanme Axis

1.9 1.10 1.10

Distance between Two Points Lying on the Line Parallel to One of the Axes

1.10

Distance between Two Points

1.10

Concept Application Exercise 1.2 Section Formula

Concept Application Exercise Sphere

1.3

Concept Application Exercise

1.4

Exercises Single Correct Answer Type Answers Key Introduction to Vectors

Coordinate Axes and Coordinate Planes in Three-Dimensional Space Coordinates of a Point in Space Distance between Two Points Section Formula

1.12 1.13 1.17 1.18

General Equation of Sphere

2.

1.1-1.23

1.19

1.21 1.22 1.22 1.23 2.1-2.64 2.1

2.1 2.2 2.2

Vector Concept

2.3

Definition

2.4

Position Vector

2.4

iv

Contents

Direction Cosines and Direction Ratios

2.4 2.5 2.6 2.11 2.14 2.15 2.17

Types of Vectors Addition of Vectors

Components of a Vector Multiplication of a Vector by a

Scalar

Vector Joining Two Points Section Formula Vectors Vector Along the Bisector of Given Two

Concept Application Exercise 2.1

2.26 2.27 2.29

Linear Combination of Vectors

2.29

Linear Combination of Vectors

2.29

Linearly Independent Vectors

2.30

Linearly Dependent Vectors

2.41

Concept Application Exercise 2.2 Solved Examples

2.42

2.55

Exercises

2.55

Single Correct Answer Type

2.59

Multiple Correct Answers Type

.60

Linked Comprehension Tpe

2.62

Matrix Match 7ype Numerical Value Type

2.62

2.63

Archives

2.64

Answers Key 3.

3.1-3.107

Different Products of Vectors Dot (Scalar) Product of Vectors

3.1 3.1

Product

Physical Interpretation of Scalar Product Geometrical Interpretation of Scalar Product Properties of Dot (Scalar) Applications of Dot (Scalar) Product 3.1 Concept Application Exercise Vector (or Cross) Product of Two Vectors Properties of Cross Product as Physical nterpretation of Cross Product Geometric Interpretation of Cross Product

Concept Application Exercise 3.2 Scalar Triple Product Geometrical Interpretation Volume of Tetrahedron Properties of Scalar Triple Product

3.1 3.2

3.3 3.18 3.20 3.21

a

Moment of Force

3.21 22

3.35 3..36 3.37 3.38 3.38

Contents Vector Triple Product

3.46 3.47

Lagrange's Identity

Reciprocal System of Vectors

3.55

Properties

3.55

Concept Application Exercise 3.3

3.58

Sohved Examples

3.60

Exercises

3.77

Single Correct Answer Type

3.77

Multiple Correct Answers Type

3.87

Linked Comprehension Type

3.92

Matrix Match Type

3.96 3.99

Numerical Value Type

3.100

Archives

3.106

Answers Key 4.

V

4.1-4.88

Line and Plane

4.1

Direction Cosines and Direction Ratios

4.1

Direction Ratios

Concept Application

4.7

Exercise 4.1

4.7

Line in Space

Equation of Straight Line Passing through a

Given Point and Parallel to

a

Given Vector

Equation of Line Passing Through Two Given Points Angle between Two Lines

4.14

4.18

Shortest Distance between Two Lines

4.24 4.26 4.26

Concept Application Exercise 4.2 Plane in Space Equation of a Plane in Normal Form

Passing through a Given Point and Normal to a Given Vector Equation of a Plane Passing through Three Given Points Equation of the Plane that Passes through Point A with Position Vector a and is Plane

4.28

4.29 4.31

Parallel to Given Vectors b and c Cartesian Form Equation of a Plane Passing through

4.9 .16

Point and Line

Equation of a

4.7

4.31 a

Given Point and Line

4.32

Intercept Form of a Plane

4.33

Equation of a Plane Passing through Two Parallel Lines

4.33

Equation of a Plane Parallel to a Given Plane Angle between Two Planes

4.33 4.34

Line of Intersection of Two Planes

4.35

vi Contents

Angle between a Line and a Plane Equation of a Plane Passing through the Line of Intersection of Two Planes

4.40 4.41

Distance of a Point from a Plane

4.43 4.45 4.48 4.50 4.51 4.51

Distance between Parallel Planes

Equation of a Plane Bisecting the Angle between Two Planes Two Sides of a Plane Regular Tetrahedron

Angle between any Edge and Face not Containing that Edge of Regular Tetrahedron Angle between the Two Faces of Regular Tetrahedron

4.51

Height of Regular Tetrahedron

4.52

Concept Application Exercise 4.3

4.53

Solved Examples

4.54 4.68

ExercisesS Single Correct Answer Type

Multiple Correct Answers 1ype Linked Comprehension Type Matrix Match Type

.68

4.77 .79 80

Archives

4.81 4.82

Answers Key

4.87

Numerical Value Type

Solutions

S.1-5.94

Chapter 1

S.1

Chapter 2

S.6

Chapter 3

S.21

Chapter 4

S.62

Appendix 1:

Chapterwise Solved January 2019 JEE Main Questions (All Sets)

A.l-A.3