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JEE Mains 8-Apr-2023 Shift 2 Solved Paper
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© examsnet.com
Question : 4
Total: 90
The area of the quadrilateral
ABCD
with vertices
A
(
2
,
1
,
1
)
,
B
(
1
,
2
,
5
)
,
C
(
−
2
,
−
3
,
5
)
and
D
(
1
,
−
6
,
−
7
)
is equal to
[8-Apr-2023 shift 2]
54
9
√
38
48
8
√
38
Validate
Solution:
Vector Area
=
→
v
=
1
2
→
AB
×
→
AC
+
1
2
→
AC
×
→
AD
=
1
2
(
→
AB
−
→
AD
)
×
→
AC
(
→
AB
=
−
^
i
+
^
j
+
4
^
k
→
AD
=
−
^
i
−
7
^
j
−
8
^
k
→
AC
=
−
4
^
i
−
4
^
j
+
4
^
k
)
=
1
2
(
8
^
j
+
12
^
k
)
×
(
−
4
)
(
^
i
+
^
j
−
^
k
)
=
1
2
|
^
i
^
j
^
k
0
8
12
1
1
−
1
|
=
(
−
2
)
(
−
20
^
i
+
12
^
j
−
8
^
k
)
=
8
(
5
^
i
−
3
^
j
+
2
^
k
)
∴
Area
=
|
→
v
|
=
8
√
25
+
9
+
4
=
8
√
38
Ans.
© examsnet.com
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