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JEE Main Math Class 12 Vector Algebra Part 3 Questions
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© examsnet.com
Question : 2
Total: 70
Let
ABC
be a triangle of area
15
√
2
and the vectors
→
A
B
=
^
i
+
2
^
j
−
7
^
k
,
→
B
C
=
a
^
i
+
b
^
j
+
c
^
k
and
→
AC
=
6
^
i
+
d
^
j
−
2
^
k
,
d
>
0
. Then the square of the length of the largest side of the triangle
ABC
is
[4 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
Area
=
1
2
|
^
i
^
j
^
k
1
2
−
7
6
d
−
2
|
=
15
√
2
(
−
4
+
7
d
)
^
i
−
^
j
(
−
2
+
42
)
+
^
k
(
d
−
12
)
(
7
d
−
4
)
2
+
(
40
)
2
+
(
d
−
12
)
2
=
1800
50
d
2
−
80
d
−
40
=
0
5
d
2
−
8
d
−
4
=
0
5
d
2
−
10
d
−
2
d
−
4
5
d
(
d
−
2
)
+
2
(
d
−
2
)
=
0
d
=
2
or
d
=
−
2
5
∵
d
>
0
,
d
=
2
(
a
+
1
)
^
i
+
(
b
+
2
)
^
j
+
(
c
−
7
)
^
k
=
6
^
i
+
2
^
j
−
2
^
k
a
+
1
=
6
&
b
+
2
=
2
,
c
−
7
=
−
2
a
=
5
b
=
0
c
=
5
|
AB
|
=
√
1
+
4
+
49
=
√
54
|
BC
|
=
√
25
+
25
=
√
50
|
AC
|
=
√
86
+
4
+
4
=
√
44
Ans. 54
© examsnet.com
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