This shows that AB
uuur
 and CD
uuur
 are collinear Alternatively, 
1
AB
2CD
  
uuur
uuur
 which implies that AB and CD
uuur
uuur  are collinear vectors Example 28 Let 
,
a band
c
rr
r  be three vectors such that |
| 3, |
| 4, | | 5
a
b
c
=
=
=
r
r
r
 and
each one of them being perpendicular to the sum of the other two, find |
a b c|
+ +
r
r
r Solution Given 
(
)
a
b
c
⋅
r+
r
r  = 0,
(
)
0,
(
)
0