Vectors Definition: A vector quantity is one which has both magnitude and direction One of the simplest vectors is displacement… it has an associated distance (magnitude) and direction. For example, if we have two points A and B then ‘displacement AB’ is a vector quantity. It can be conveniently represented by a straight line joining A and B, and the direction indicated by an arrow. A B

The length of the line AB represents the distance between A and B. For ‘vector AB’ we write either AB or and textbooks use bold type. Another notation involves the use of lower case letters r ‘vector r’

Definition: A scalar quantity is one which has magnitude only. In the context of the previous example ‘distance travelled’ is a scalar quantity. A displacement vector in two dimensions is conveniently expressed in component form a d c b

In General Addition and Subtraction using components We can see displacement a followed by displacement b which is… entirely equivalent to the single displacement c. We writec = a + b

Multiplication of a vector by a scalar Consider the vectors a, 3a, -a, -2a a 3a3a -a-a -2a They are parallel vectors

Modulus of a vector: is its magnitude and hence a scalar. The modulus of a is written |a| and is written usually as a. Magnitude of a vector in component form Example a In general

Parallel vectors (1)If a and b are parallel then for some scalar quantity,, it must follow that a = b (2)If a = b then a and b are parallel