Solution We have 
2
2
|
|
1
2
5
a =
+
=
r
 and 
2
2
|
|
2
1
5
b  
 
 
r
So, |
| |
|
a
=b
r
r But, the two vectors are not equal since their corresponding components
are distinct Example 6 Find unit vector in the direction of vector 
ˆ
ˆ
ˆ
2
3
a
i
j
k
=
+
+
r
Solution The unit vector in the direction of a vector ar  is given by 
1
ˆ
|
|
a
=aa
rr Now
|
|
ar  =
2
2
2
2
3
1
14
+
+
=
Therefore
1
ˆ
ˆ
ˆ
ˆ
(2
3
)
14
a
i
j
k
=
+
+
 =
2
3
1
ˆ
ˆ
ˆ
14
14
14
i
j
k
+
+
Example 7 Find a vector in the direction of vector 
ˆ
2ˆ
a
i
j
r= −
 that has magnitude
7 units