A vector is represented by a line with an arrow head.The length of the line gives the magnitude and the arrow head represents the direction of the vector.On a paper,vector quantity is represented by
→
placing an arrow on the corresponding letter as p.
The magnitude of the vector is called the modulus (mod) of vector P
and is represented by|p| or simply p (without the sing of vector on it.)
A vector may also be written as AB where A is the starting point and
B.represent the terminating point or the ending point AB represents
that this vector starts at A and ends at B.The length of AB gives the
magnitude and its direction is from A towards B.
Type of Vectors
Vectors can be divided into the following types.
1. Negative Vector :The negative of a vector is defined as another vector having same magnitude as that of given vector but drawn in opposite direction.i.e.,any vector p and its negative vector (-P) are as shown:
2. Equal vector : Two or more vector are said to be equal,if they have same magnitude and direction. It P and Q are two equal vectors then,
→ →
P = Q
3. Unit Vector : A vector divided by its magnitude is called a unit vector.It has magnitude one unit and direction same as the direction of given vector.It is denoted by P.
→
P
P =
P
unit vectors along the three mutually perpendicular axis are represented by i.j and k.
i is the unit vector along x-axis.
j is the unit vector along y-axis.
k is the unit vector along z-axis.
i.j and k are mutually perpendicular to each other i.e.,angle between any pair is 90.
4. Co-initial Vectors : Two or more vectors having same initial or starting point are called co-initial vectors 'a','b','c','d' and E vector are five vectors having same initial point.
5.Collinear Vector : Two or more vectors having equal or unequal magnitudes,which act either along the some line or along the parallel lines are called collinear vectors.
6. Zero vector : A vector having zero magnitude and arbitrary direction is called zero vector. It is dented by 'o'.
Thus,zero vector is insignificant in vector algebra.
(iii) Some common terms used in vector algebra.
7. Vectors in same order : Two or more vectors are said to be in same order if final point (Terminating point) of first vector coincides with the initial point of second vector.
8. Vectors in opposite order : If final points of two vectors coincide,then we say that these vectors are in opposite order.
9. Resultant vector : Resultant of two or more vectors is a single vector which produces the same effect as the individual vectors together do.
→
placing an arrow on the corresponding letter as p.
The magnitude of the vector is called the modulus (mod) of vector P
and is represented by|p| or simply p (without the sing of vector on it.)
A vector may also be written as AB where A is the starting point and
B.represent the terminating point or the ending point AB represents
that this vector starts at A and ends at B.The length of AB gives the
magnitude and its direction is from A towards B.
Type of Vectors
Vectors can be divided into the following types.
1. Negative Vector :The negative of a vector is defined as another vector having same magnitude as that of given vector but drawn in opposite direction.i.e.,any vector p and its negative vector (-P) are as shown:
2. Equal vector : Two or more vector are said to be equal,if they have same magnitude and direction. It P and Q are two equal vectors then,
→ →
P = Q
3. Unit Vector : A vector divided by its magnitude is called a unit vector.It has magnitude one unit and direction same as the direction of given vector.It is denoted by P.
→
P
P =
P
unit vectors along the three mutually perpendicular axis are represented by i.j and k.
i is the unit vector along x-axis.
j is the unit vector along y-axis.
k is the unit vector along z-axis.
i.j and k are mutually perpendicular to each other i.e.,angle between any pair is 90.
4. Co-initial Vectors : Two or more vectors having same initial or starting point are called co-initial vectors 'a','b','c','d' and E vector are five vectors having same initial point.
5.Collinear Vector : Two or more vectors having equal or unequal magnitudes,which act either along the some line or along the parallel lines are called collinear vectors.
6. Zero vector : A vector having zero magnitude and arbitrary direction is called zero vector. It is dented by 'o'.
Thus,zero vector is insignificant in vector algebra.
(iii) Some common terms used in vector algebra.
7. Vectors in same order : Two or more vectors are said to be in same order if final point (Terminating point) of first vector coincides with the initial point of second vector.
8. Vectors in opposite order : If final points of two vectors coincide,then we say that these vectors are in opposite order.
9. Resultant vector : Resultant of two or more vectors is a single vector which produces the same effect as the individual vectors together do.