Now
a
b
×
r
r
 =
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
3
1
4
5
4
1
1
1
i
j
k
i
j
k
=
+
−
−
Therefore
|
|
a
b
×
r
r
 =
25 1 16
42
+ +
=
and hence, the required area is 
42 EXERCISE 10 4
1 Find 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
|
|,  if  
7
7
and
3
2
2
a b
a
i
j
k
b
i
j
k
×
= −
+
=
−
+
r
r
r
r