The area of the given triangle
is 1 | AB AC |
2
uuur×
uuur Now,
AB AC
×
uuur
uuur  =
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
0
1
2
4
2
1
2
0
i
j
k
i
j
k
= −
+
−
Therefore
| AB AC|
uuur×
uuur  =
16
4
1
21
+
+ =
Thus, the required area is 
1
21
2
© NCERT
not to be republished
 MATHEMATICS
454
Example 25 Find the area of a parallelogram whose adjacent sides are given
by the vectors 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
3
4
and
a
i
j
k
b
i
j
k
=
+
+
= −
+
r
r
Solution The area of a parallelogram with 
aand
rb
r
 as its adjacent sides is given
by |
|
a
×b
r
r 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