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UPSC NDA Math Model Paper 8
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© examsnet.com
Question : 5
Total: 120
The area of the parallelogram whose diagonals are
→
a
=
3
^
i
+
^
j
−
2
^
k
and
→
b
=
^
i
−
3
^
j
+
4
^
k
is:
10
√
3
5
√
3
10
√
2
5
√
2
Validate
Solution:
The given diagonals of the parallelogram are
→
a
=
3
^
i
+
^
j
−
2
^
k
and
→
b
=
^
i
−
3
^
j
+
4
^
k
Using the formula for the area of a parallelogram whose diagonals
→
a
and
→
b
are given, we get:
Area
=
1
2
|
→
a
×
→
b
|
=
1
2
|
(
a
2
b
3
−
a
3
b
2
)
^
i
+
(
a
3
b
1
−
a
1
b
3
)
^
j
+
(
a
1
b
2
−
a
2
b
1
)
^
k
|
=
1
2
√
(
a
2
b
3
−
a
3
b
2
)
2
+
(
a
3
b
1
−
a
1
b
3
)
2
+
(
a
1
b
2
−
a
2
b
1
)
2
=
1
2
√
[
(
1
)
(
4
)
−
(
−
2
)
(
−
3
)
]
2
+
[
(
−
2
)
(
1
)
−
(
3
)
(
4
)
]
2
+
[
(
3
)
(
−
3
)
−
(
1
)
(
1
)
]
2
=
1
2
√
(
4
−
6
)
2
+
(
−
2
−
12
)
2
+
(
−
9
−
1
)
2
=
1
2
√
4
+
196
+
100
=
1
2
√
300
=
5
√
3
© examsnet.com
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