� For a given vector ar , the vector ˆ
|
a|
a
=a
r
r  gives the unit vector in the direction
of ar � The position vector of a point R dividing a line segment joining the points
P and Q whose position vectors are 
aand
rb
r
 respectively, in the ratio m : n
(i)
internally, is given by na
mmb
+n
+
r
r (ii)
externally, is given by mb
na
m
−n
−
r
r � The scalar product of two given vectors 
aand
rb
r
 having angle θ between
them is defined as
|
||
| cos
a b
a b
⋅
=
θ
r
r
r
r