a a
a b
b a
b b
−
⋅
−
⋅
+
⋅
r
r
r r
r r
r
r
© NCERT
not to be republished
 MATHEMATICS
446
B
C
A
a
b
+
a
b
=
2
2
|
|
2(
) |
|
a
a b
b
−
⋅
+
r
r
r
r
=
2
2
(2)
2(4)
(3)
−
+
Therefore
|
|
a
−b
r
r
 =
5
Example 18 If ar  is a unit vector and (
) (
)
8
x
a
x
a
−
⋅
+
=
r
r
r
r
, then find |
|
xr Solution Since ar  is a unit vector, |
ra =| 1 Also,
(
) (
)
x
a
x
a
−
⋅
+
r
r
r
r  = 8
or
x x
x a
a x
a a
⋅
+
⋅
−
⋅
−
⋅
r r
r r
r r
r r  = 8
or
2
|
|
1
rx
 = 8  i e