� 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 Also, when a b
⋅
rr
 is given, the angle ‘θ’ between the vectors 
aand
rb
r
 may be
determined by
cosθ = |
||
a b|
a b
⋅
rr
r
r
� If θ is the angle between two vectors 
aand
rb
r
, then their cross product is
given as
a
b
×
r
r
=
ˆ
|
||
a b|sin
n
θ
r
r
where ˆn is a unit vector perpendicular to the plane containing 
aand
rb
r