المتجهات

1-6 Multiplying of Vectors
(1) Scalar Product (dot product)
Let and are two vectors. The scalar product of , is
=
Where : is the magnitude of
is the magnitude of
is the angle between and
The quantity obtained from the scalar product is a scalar quantity. For example, the work is a scalar quantity obtained from the product of tow vectors (displacement and the component of force in the direction of this displacement);
Now, from: =
(1) if =0 then cos(0)=1 and =AB
(2) if =90 then cos(90)=0 and =0


(*) Properties of Scalar Product (Dot Product)
(a) = (b) ( ) = +
(c) = 2 (parallel vectors) (d) (- )= -A2 (anti parallel vectors)
Using the unit vector , , we obtain:
. = cos(0) =(1)(1)(1) = 1 where i=i , j=j , k=k , = 1
. = cos(90) = (1)(1)(0) = 0 where i.j , j.k , i.k ,= 0