Vector and 3-D Geometry : Course in Mathematics for the IIT-JEE and Other Engineering Entrance Examinations

Cover
VECTORS AND 3D-GEOMETRY
	COPYRIGHT
CONTENTS
PREFACE
PART A VECTOR
	Vector Algebra 1
		BASIC CONCEPTS
			Directed Line Segment
			Characterization Of A Directed Line Segment
			Types Of Vectors
			Section Formula
			Linearly Dependent And Independent Set Of n Vectors
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTIONS WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANTIONS
	Vector Algebra 2
		BASIC CONCEPTS
			Rectangular Components Of The Vector
			Angle Between Sides Of A Triangle ABC
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise
		ANSWERS
			Exercise
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTIONS WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Dot Product Of Vector
		BASIC CONCEPTS
			Dot Product Or Scalar Product
			Angle Between Two Vectors
			Geometrical Interpretation Of Scalar Product Or Projection And Component Of A Vector
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			EXERCISE 1
			EXERCISE 2
		ANSWERS
			EXERCISE 1
			EXERCISE 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		SOLUTIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Vector Product
		BASIC CONCEPTS
			Geometrical Interpretation Of Cross Product
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Vector Triple Product
		BASIC CONCEPTS
			Scalar Triple Products
			Vector Triple Product
			Geometrical Interpretation Of Vector Triple Product: a×(b×c)
			Scalar Product Of Four Vectors
			Vector Product Of Four Vectors
			Reciprocal System Of Vectors
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
	Geometrical Applications Of Vector
		BASIC CONCEPTS
			Some Important Results Connected With A Straight Line
			Some Important Results Connected With A Plane
			Some Important Results Connected With A Sphere
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		SOLUTIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Test Your Skills
		ASSERTION/REASONING
			Assertion And Reasoning Type Questions
		ASSERTION/REASONING SOLUTIONS
		MENTAL PREPARATION TEST 1
		MENTAL PREPARATION TEST 2
		TOPICWISE WARMUP TEST 1
		TOPICWISE WARMUP TEST 2
		TOPICWISE WARMUP TEST 3
		TOPICWISE WARMUP TEST 1: SOLUTION
		TOPICWISE WARMUP TEST 2: SOLUTION
		TOPICWISE WARMUP TEST 3: SOLUTION
		QUESTION BANK: SOLVE THESE TO MASTERS
		ANSWERS
			Lecture 1
			Lecture 2
			Lecture 3
			Lecture 4
			Lecture 5
			Lecture 6
			Lecture 7
PART B 3D-GEOMETRY
	Cartesian System Of Rectangular Co-ordinates
		BASIC CONCEPTS
			Important formulae Connected With One Point P(X,Y,Z) In Space
			Rectangular Parallelopiped Or Cuboid
			Important Formulae Connected With Two Points In Space
			Use Of Distance Formula
			Formula Connected With Three Points
			Formula Connected With Triangles
			Centroid Of A Tetrahedron
			Shifting The Origin (translation Of The Axes)
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		HINTS AND EXPLANATIONS
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Direction Cosines And Direction Ratios
		BASIC CONCEPTS
			Direction Cosine's Of A Straight Line
			Direction Ratios Or Direction Numbers Of A Straight Line
			Angle Between Two Intersecting Lines
			Perpendicular Distance Of A Point P (X, Y, Z) From A Line Passing Through Points A (X, Y, Z) And B (X, Y, Z)
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Plane
		BASIC CONCEPTS
			List Or Important Formula Connected With One Plane
			The Plane
			Pair Of Planes
	Plane I
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Plane II
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Straight Line
		BASIC CONCEPTS
			List Of Important Formula Connected With One Straight Line In Space
				General Equation Of A Straight Line
				Symmetrical Form Of The Equation Of A Line Or The Distance Form Of The Equation Of A Line
				Equation Of A Straight Line Through Two Given Points
				T Ransformation Of General Form Equation Of A Straight Line To Symmetrical Form
				Length of the Perpendicular (P) From aPoint A (a, b, l) To a Given Line
				Results Connected With A Plane And A Straight Line
				Results Connected With Two Straight Lines
		Shortest Distance Between Two Skew (non-coplanar) Lines
	Equation Of A Line in Space
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			EXERCISE 1
			EXERCISE 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Plane And Straight Line Combined In Space
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Sphere
		BASIC CONCEPTS
			Definition
			Central Form Equation Of The Sphere
			Standard Equation Of The Sphere
			General Equation Of The Sphere
			Diametral Form Equation Of Sphere
			Position Of A Point P(X1, Y1, Z1) With Respect to Sphere X2 + Y2 + Z2 = R2
			Important Results Connected With A Plane
			Important Results Connected With Two Spheres
		SOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): FOR BETTER UNDERSTANDING AND CONCEPT BUILDING OF THE TOPIC
		UNSOLVED SUBJECTIVE PROBLEMS (XII BOARD (C.B.S.C./STATE)): TO GRASP THE TOPIC SOLVE THESE PROBLEMS
			Exercise 1
			Exercise 2
		ANSWERS
			Exercise 1
			Exercise 2
		SOLVED OBJECTIVE PROBLEMS: HELPING HAND
		OBJECTIVE PROBLEMS: IMPORTANT QUESTION WITH SOLUTIONS
		HINTS AND EXPLANATIONS
		UNSOLVED OBJECTIVE PROBLEMS (IDENTICAL PROBLEMS FOR PRACTICE): FOR IMPROVING SPEED WITH ACCURACY
		WORKSHEET: TO CHECK THE PREPARATION LEVEL
			Important Instructions
		WORKSHEET
		HINTS AND EXPLANATIONS
	Test Your Skills
		ASSERTION/REASONING
			Assertion And Reasoning Type Questions
		ASSERTION/REASONING: SOLUTIONS
		MENTAL PREPARATION TEST 1
		MENTAL PREPARATION TEST 2
		TOPICWISE WARMUP TEST 1
		TOPICWISE WARMUP TEST 2
		TOPICWISE WARMUP TEST 1: SOLUTIONS
		TOPICWISE WARMUP TEST 2: SOLUTIONS
		QUESTION BANK: SOLVE THESE TO MASTERS
		ANSWERS
			Lecture 1
			Lecture 2
			Lecture 3 a
			Lecture 3 b
			Lecture 4 a
			Lecture 4 b
			Lecture 5
			Lecture 6