13 April 2010

Vectors

Vectors are very important in Physics and especially in physics problems. Why?
Because many physical quantities, such as velocity, acceleration, force, electric field, magnetic field, and others are vectors.
 
Vectors carry the information about magnitude and direction of physical quantity. 
For example, we know the vector of velocity. It means that we know the direction of the motion and the magnitude of velocity (speed).

Properties of vectors

* two vectors are equal if they are equal in both magnitude and direction:

 

* addition of two vectors:

 

* multiplication by a number
Vector (where is the positive number) has the same direction as vector , but its length is times larger then the length of vector .
Vector (where is the negative number) has the direction opposite to the direction of vector , but its length is times larger then the length of vector

  

 

* scalar (dot) product
is a scalar (not vector) =



















If the vectors are orthogonal then the scalar product is 0 







* vector product


is a VECTOR, the magnitude of which is

Vector is orthogonal to the plane formed by vectors and .









If two vectors have the same direction then vector product is 0