10 If 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2
2
3 ,
2
and
3
a
i
j
k
b
i
j
k
c
i
j
=
+
+
= − +
+
=
+
r
r
r
are such that a
+ λb
r
r
 is
perpendicular to cr , then find the value of λ 11 Show that |
|
|
|
a b
r+b a
r
r
r  is perpendicular to |
|
|
|
a b
r−b a
r
r
r , for any two nonzero
vectors 
aand 
rb
r