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JEE Main Math Class 12 Vector Algebra Part 3 Questions
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© examsnet.com
Question : 9
Total: 70
30. Let
→
a
=
2
^
i
−
3
^
j
+
4
^
k
,
→
b
=
3
^
i
+
4
^
j
−
5
^
k
, and a vector
→
c
be such that
→
a
×
(
→
b
+
→
c
)
+
→
b
×
→
c
=
^
i
+
8
^
j
+
13
^
k
. If
→
a
⋅
→
c
=
13
, then
(
24
−
→
b
⋅
→
c
)
is equal to ______.
[6 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
→
a
×
→
b
+
→
a
×
→
c
+
→
b
×
→
c
=
(
1
,
8
,
13
)
→
a
×
(
→
a
×
→
b
)
+
→
a
×
(
→
a
×
→
c
)
+
→
a
×
(
→
b
×
→
c
)
=
→
a
×
(
^
i
+
8
^
j
+
13
^
k
)
(
→
a
⋅
→
b
)
→
a
−
a
2
→
b
+
(
→
a
⋅
→
c
)
→
a
−
a
2
→
c
+
(
→
a
⋅
→
c
)
→
b
−
(
→
a
⋅
→
b
)
→
c
=
→
a
×
(
^
i
+
8
^
j
+
13
^
k
)
⇒
−
26
→
a
−
29
→
b
+
13
→
a
−
29
→
c
+
13
→
b
+
26
→
c
=
→
a
×
(
^
i
+
8
^
j
+
13
^
k
)
⇒
−
13
→
a
−
16
→
b
−
3
→
c
=
→
a
×
(
^
i
+
8
^
j
+
13
^
k
)
⇒
−
13
→
a
⋅
→
b
−
16
b
2
−
3
→
b
⋅
→
c
=
{
→
a
×
(
^
i
+
8
^
j
+
13
^
k
)
}
⋅
→
b
⇒
(
−
13
)
(
−
26
)
−
16
(
50
)
−
3
→
b
⋅
→
c
=
|
2
−
3
4
1
8
13
3
4
−
5
|
⇒
−
462
−
3
→
b
⋅
→
c
=
−
396
⇒
→
b
⋅
→
c
=
−
22
Hence
24
−
→
b
⋅
→
c
=
46
© examsnet.com
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