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Vector Algebra Part 3
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Section:
Mathematics
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© examsnet.com
Question : 13
Total: 54
Let
→
a
=
2
^
i
−
^
j
+
3
^
k
,
‌
‌
→
b
=
3
^
i
−
5
^
j
+
^
k
and
→
c
be a vector such that
→
a
×
→
c
=
→
c
×
→
b
and
(
→
a
+
→
c
)
â‹…
(
→
b
+
→
c
)
=
168
. Then the maximum value of
|
→
c
|
2
is
[29 Jan 2025 Shift 1]
308
462
154
77
Validate
Solution:
👈: Video Solution
‌
→
a
×
→
c
=
→
c
×
→
b
=
−
(
→
b
×
→
c
)
‌
⇒
(
→
a
×
→
c
+
→
b
×
→
c
)
=
(
→
a
+
→
b
)
×
→
c
=
0
‌
⇒
→
c
‌
is parallel to
‌
→
a
+
→
b
‌
→
c
=
λ
(
5
∧
i
+
(
−
6
)
∧
j
+
4
∧
k
)
⇒
|
→
c
|
2
=
λ
2
(
Ï€
)
‌
(
→
a
+
→
c
)
â‹…
(
→
b
+
→
c
)
=
→
a
â‹…
→
b
+
|
→
c
|
2
+
→
c
â‹…
(
→
a
+
→
b
)
‌
=
(
6
+
5
+
3
)
+
|
→
c
|
2
+
λ
(
25
+
36
+
16
)
=
168
‌
⇒
|
→
c
|
2
+
λ
(
77
)
=
154
‌
⇒
77
λ
2
+
77
λ
−
152
=
0
‌
⇒
λ
2
+
λ
−
2
=
0
‌
⇒
(
λ
+
2
)
(
λ
−
1
)
=
0
‌
|
→
c
|
max
2
=
(
−
2
)
2
(
77
)
=
308
© examsnet.com
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