Vectors Mathematics, Types of Vectors, Math Assignment Help

mathematics - Vectors Mathematics, Types of Vectors, Math

Scalars and vectors: Those quantities which have only magnitude and are not related to any direction in space are called scalars whereas those which have both magnitude and direction are called vector quantities.

Modulus of a vector: A non­negative number which is the measure of the magnitude of a vector is called its modulus or module. The modulus of a vector a is written as | a | = a.

Note: We are denoting a vector by bold letters. So  or  ¯a are same.

Types of Vectors: 

(i)      Null vector or zero vector: If the initial and terminal points of a vector coincide, then it is called a zero vector. It is denoted by  or 0. Its magnitude is zero and direction indeterminate.

(ii)     Unit vector: A vector whose magnitude is of unit length along any vector a is called a unit vector in the direction of a and is denoted by .Clearly

(iii)    Reciprocal vector: A vector whose direction is same as that of a given vector a but its magnitude is the reciprocal of the magnitude of the given vector a is called the reciprocal of a and is denoted by a-1.

                    Thus if a = a. , then a-1 = - -(1/a)ã    .

(iv)    Equal vector: Two vectors a and b are said to equal if they have same magnitude, the same or parallel support and the same sense of direction and written as a = b.

Obviously if  = , then â =  b.

Note: The equality of two vectors does not depend on the absolute position of their ends.

(v)     Negative of a vector: A vector having the same magnitude as that of a given vector a and direction opposite to that of a, is called the negative of a and denoted by - a.

Thus if  Vector AB = a, then - a =     Vector BA

(vi)    Collinear vector: Two or more vectors are said to be collinear or parallel if they have the same or parallel support.

(vii)   like and unlike vectors : Collinear vectors having the same direction are known as like vectors while those having opposite direction are known as unlike vectors.

(Viii)  Coplanar vectors: Any number of vectors are said to be coplanar when they are parallel to the same plane.

(ix)    Co-initial vector: Vectors having the same initial point are known as co-initial vectors.

(x)     Localised vectors and free vectors: A vector drawn parallel to a given vector through a specified point as the initial point, is known as a localised vector. If the initial point of a vector is not specified, it is said to be a free vector.

(xi)    Position vector: Let 0 be the origin and let A be a point such that  Vector OA = a, then we say that the position vector of A is a.

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