(2)
Similarly
a c
b c
⋅
+
r⋅
r r
r  = – 4 (3)
Adding (1), (2) and (3), we have
2 (
)
a b
b
a
c
c
⋅
+
⋅ +
⋅
r
r
r
r
r
r
 = – 21
or
2μ = – 21, i e , μ =
221
−
Example 30 If with reference to the right handed system of mutually perpendicular
unit vectors 
ˆ
ˆ
ˆ ˆ
ˆ
ˆ
ˆ
ˆ
,
 and ,
3
,  
2
– 3
i
j
k
i
j
i
j
k
α =
−
β =
+
r
r
, then express β
r  in the form
1
2
, where  1
   
  
 
r
r
r
r
is parallel to 
  and  2
r
r
 is perpendicular to αr