Solution We have
 AB
uuur  =
ˆ
ˆ
ˆ
(1
2)
( 3 1)
( 5 1)
i
j
k
−
+ − +
+ − −
ˆ
ˆ
2ˆ
6
i
j
k
  
 
 
  BC
uuur  =
ˆ
ˆ
ˆ
(3 1)
( 4
3)
( 4
5)
i
j
k
−
+ − +
+ − +
ˆ
ˆ
ˆ
2i
j
k
=
−
+
and
CA
uuur
 =
ˆ
ˆ
ˆ
(2
3)
( 1
4)
(1
4)
i
j
k
−
+ − +
+
+
 
ˆ
ˆ
3ˆ
5
i
j
k
= − +
+
Fig 10 17
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not to be republished
 MATHEMATICS
440
Further, note that
| AB|2
uuur
 =
2
2
41
6
35 | BC |
| CA |
=
+
=
+
uuur
uuur
Hence, the triangle is a right angled triangle EXERCISE 10 2
1