Flashcards: Vector Algebra | Mathematics (Maths) for JEE Main & Advanced PDF Download

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VECTOR ALGEBRA 
Vector algebra deals with addition / subtraction / product of vector quantities. Application of vectors to 
many as geometrical problems cuts short the procedure. Hence geometrical significance of vectors 
should be well understood. 
  
Page 2


 
 
 
 
VECTOR ALGEBRA 
Vector algebra deals with addition / subtraction / product of vector quantities. Application of vectors to 
many as geometrical problems cuts short the procedure. Hence geometrical significance of vectors 
should be well understood. 
  
 
 
 
 
 
VECTORS AND SCALARS 
The physical quantities (we deal with) are generally of two types: 
Scalar Quantity : A quantity which has magnitude but no sense of direction is called Scalar quantity (or 
scalar), e.g., mass, volume, density, speed etc. 
Vector Quantity : A quantity which has magnitude as well as a sense of direction in space is called a 
vector quantity, e.g., velocity, force, displacement etc. 
  
Page 3


 
 
 
 
VECTOR ALGEBRA 
Vector algebra deals with addition / subtraction / product of vector quantities. Application of vectors to 
many as geometrical problems cuts short the procedure. Hence geometrical significance of vectors 
should be well understood. 
  
 
 
 
 
 
VECTORS AND SCALARS 
The physical quantities (we deal with) are generally of two types: 
Scalar Quantity : A quantity which has magnitude but no sense of direction is called Scalar quantity (or 
scalar), e.g., mass, volume, density, speed etc. 
Vector Quantity : A quantity which has magnitude as well as a sense of direction in space is called a 
vector quantity, e.g., velocity, force, displacement etc. 
  
 
 
 
 
 
NOTATION AND REPRESENTATION OF 
VECTORS 
Vectors are represented by ?? ? , ?? ? ?
, ?? ? and their magnitude (modulus) is represented by ?? , ?? , ?? , or | ?? ? | , | ?? ? ?
| , | ?? ? | , … 
The vectors are represented by directed line segments. 
For example, line segment ????
? ? ? ? ? ?
 represents a vector with magnitude ???? (length of line segment), arrow 
denotes its direction. ?? is initial point and ?? is terminal point. 
  
Page 4


 
 
 
 
VECTOR ALGEBRA 
Vector algebra deals with addition / subtraction / product of vector quantities. Application of vectors to 
many as geometrical problems cuts short the procedure. Hence geometrical significance of vectors 
should be well understood. 
  
 
 
 
 
 
VECTORS AND SCALARS 
The physical quantities (we deal with) are generally of two types: 
Scalar Quantity : A quantity which has magnitude but no sense of direction is called Scalar quantity (or 
scalar), e.g., mass, volume, density, speed etc. 
Vector Quantity : A quantity which has magnitude as well as a sense of direction in space is called a 
vector quantity, e.g., velocity, force, displacement etc. 
  
 
 
 
 
 
NOTATION AND REPRESENTATION OF 
VECTORS 
Vectors are represented by ?? ? , ?? ? ?
, ?? ? and their magnitude (modulus) is represented by ?? , ?? , ?? , or | ?? ? | , | ?? ? ?
| , | ?? ? | , … 
The vectors are represented by directed line segments. 
For example, line segment ????
? ? ? ? ? ?
 represents a vector with magnitude ???? (length of line segment), arrow 
denotes its direction. ?? is initial point and ?? is terminal point. 
  
 
 
 
SOME SPECIAL VECTORS 
1 Null vectors : A vector with zero magnitude and indeterminate direction, denoted by 0
? ?
 is called null 
vector or zero vector. 
2 Unit vector : A vector with unit magnitude (one unit), denoted by ?? ˆ where | ?? ˆ | = 1 unit is called unit 
vector. 
3 Equal vectors : Two vectors ?? ? and ?? ? ?
 are said to be equal if they have same sense of direction and 
| ?? ? | = | ?? ? ?
|, denoted by ?? ? = ?? ? ?
. 
4 Like and unlike vectors : Vectors having same sense of directions are called Like vectors and 
opposite sense of directions are called Unlike vectors. 
 
  
Page 5


 
 
 
 
VECTOR ALGEBRA 
Vector algebra deals with addition / subtraction / product of vector quantities. Application of vectors to 
many as geometrical problems cuts short the procedure. Hence geometrical significance of vectors 
should be well understood. 
  
 
 
 
 
 
VECTORS AND SCALARS 
The physical quantities (we deal with) are generally of two types: 
Scalar Quantity : A quantity which has magnitude but no sense of direction is called Scalar quantity (or 
scalar), e.g., mass, volume, density, speed etc. 
Vector Quantity : A quantity which has magnitude as well as a sense of direction in space is called a 
vector quantity, e.g., velocity, force, displacement etc. 
  
 
 
 
 
 
NOTATION AND REPRESENTATION OF 
VECTORS 
Vectors are represented by ?? ? , ?? ? ?
, ?? ? and their magnitude (modulus) is represented by ?? , ?? , ?? , or | ?? ? | , | ?? ? ?
| , | ?? ? | , … 
The vectors are represented by directed line segments. 
For example, line segment ????
? ? ? ? ? ?
 represents a vector with magnitude ???? (length of line segment), arrow 
denotes its direction. ?? is initial point and ?? is terminal point. 
  
 
 
 
SOME SPECIAL VECTORS 
1 Null vectors : A vector with zero magnitude and indeterminate direction, denoted by 0
? ?
 is called null 
vector or zero vector. 
2 Unit vector : A vector with unit magnitude (one unit), denoted by ?? ˆ where | ?? ˆ | = 1 unit is called unit 
vector. 
3 Equal vectors : Two vectors ?? ? and ?? ? ?
 are said to be equal if they have same sense of direction and 
| ?? ? | = | ?? ? ?
|, denoted by ?? ? = ?? ? ?
. 
4 Like and unlike vectors : Vectors having same sense of directions are called Like vectors and 
opposite sense of directions are called Unlike vectors. 
 
  
 
 
 
SOME SPECIAL VECTORS 
5. Negative of a vector : Negative of a vector ?? ? , denoted by - ?? ? , is a vector whose magnitude is | ?? ? | and 
direction is opposite of ?? ? . 
6. Collinear vectors : Vectors whose lines of action act along a line or parallel to a given line are called 
collinear vectors. 
7. Parallel vectors : Vectors having same line of action or are parallel to a fixed straight lines are called 
parallel vectors. 
8. Coplanar vectors: The vectors which lie in the same plane. At least three coplanar unequal vectors are 
required to make the sum zero and at least four if non-coplanar.