11 Let the vectors 
a  and  
rb
r
 be such that 
2
|
| 3  and |
|
3
a
b
=
r=
r
, then a
×b
r
r
 is a
unit vector, if the angle between   and  
a
rb
r
 is
(A) π/6
(B) π/4
(C) π/3
(D) π/2
12 Area of a rectangle having vertices A, B, C and D with position vectors
1
1
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
–
4 ,
4
2
2
i
j
k i
j
k
+
+
+
+
, 
1
ˆ
ˆ
ˆ
4
2
i
j
k
−
+
 and 
1
ˆ
ˆ
ˆ
–
4
2
i
j
k
−
+
, respectively is
(A) 1
2
(B) 1
(C) 2
(D) 4
Miscellaneous Examples
Example 26 Write all the unit vectors in XY-plane Solution Let r
x i
y j
∧
∧
=
+
r
 be a unit vector in XY-plane (Fig 10