PHYSICS : 2. Mathematical methods

Scalar

Physical quantities which can be described by their magnitude.

Vector

Physical quantities which can be completely described by their magnitude and direction.

Vector is represented by?

An arrow

Zero vector

Vector having zero magnitude with particular direction.

Resultant vector

The resultant of two or more vectors is that single vector which produces the same effect as produced by all the vectors together.

Negative vector

Two or more vector of the same magnitude but opposite direction.

Equal vector

Two or more vector having same magnitude and direction.

Position vector

A vector which gives the position of a particle at a point with respect to the origin of chosen co-ordinate system.

Unit vector

A vector having unit magnitude in a given direction.

Multiplication of vector by scalar

Forms vector quantity.

Addition and subtraction of vectors

1.when two or more vectors get added or subtracted then they must be of same physical quantity.

2. Addition or subtraction of two vector always gives another vector.

If two parallel vector are added

Direct sum

If two vector are anti parallel

Direct substraction

Law of vector addition

1. Triangle Law for vector addition

2. Law of parallelogram of vectors.

3. Polygon law.

Laws derived from triangle law

1. Commutative law.

2. Associative law.

3. Distributive law.

Scalar product

The scalar product of P^ and Q^ is written as

P^•Q^ = PQcos° [°= thita]

Where thita is the angle between P^ & Q^.

Vector cross product

P^×Q^ =PQsin°

Consist direction.

Characteristics of vector product

1.Vector product does not obey commutative law of multiplication.

2. The vector product obeys the distributive of multiplication.

3. If the two non zero vectors are parallel to each other their vector product is zero vector. °=0

4. If the two non zero vectors are anti parallel to each other their vector product is zero vector. °=180

5. If the two non zero vectors are perpendicular to each other the magnitude of their vector product is equal to the product of magnitudes of the two vectors.