Solution The sum of the given vectors is
ˆ
ˆ
ˆ
(
, say) = 4
3
2
 
 
 
 
r
r
r
a
b
c
i
j
k
and
|
|
cr  =
2
2
2
4
3
( 2)
29
+
+ −
=
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VECTOR ALGEBRA
437
Thus, the required unit vector is
1
1
4
3
2
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(4
3
2 )
|
|
29
29
29
29
c
c
i
j
k
i
j
k
=c
=
+
−
=
+
−
r
r
Example 9  Write the direction ratio’s of the vector 
ˆ
ˆ
ˆ
2
a
i
j
k
= +
−
r
 and hence calculate
its direction cosines Solution Note that the direction ratio’s a, b, c of a vector 
ˆ
ˆ
ˆ
r
xi
yj
zk
=
+
+
r
 are just
the respective components x, y and z of the vector So, for the given vector, we have
a = 1, b = 1 and c = –2 Further, if l, m and n are the direction cosines of the given
vector, then
1
1
2
,
,
  as  | |
6
|
|
|
|
|
|
6
6
6
a
b
c
l
m
n
r
r
r
r
−
=
=
=
=
=
=
r=
r
r
r
Thus, the direction cosines are 
1
1
2
,
,–
6
6
6
⎛
⎞
⎜
⎟
⎝
⎠