21
© NCERT
not to be republished
VECTOR ALGEBRA
447
Hence
|
|
a
b
 
r
r
≤ |
|
|
|
a
b
 
r
r
Remark If the equality holds in triangle inequality (in the above Example 20), i e |
|
a
b
+
r
r
 = |
|
|
|
a
+b
r
r
,
then
| AC|
uuur
 = | AB|
uuur+| BC |
uuur
showing that the points A, B and C are collinear Example 21 Show that the points 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
A( 2
3
5 ), B(
2
3 )
i
j
k
i
j
k
−
+
+
+
+
 and 
ˆ
C(7ˆ
)
i
k
−
are collinear