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# Vectors Mathematics, Types of Vectors, Math Assignment Help

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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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**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:**

**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.

**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

**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}.

^{-1}= - -(1/a)ã .

**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.

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

**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.

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

**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.

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

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

**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.

**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.

**Vectors Mathematics Assignment Help – Homework Help**