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JEE Main Math Class 12 Vector Algebra Part 2 Questions
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© examsnet.com
Question : 70
Total: 100
If
a
=
α
∧
j
+
β
∧
j
+
3
∧
k
,
b
=
−
β
∧
i
−
α
∧
j
−
∧
k
and
c
=
∧
i
−
2
∧
j
−
∧
k
such that
a
⋅
b
=
1
and
b
.
c
=
−
3
, then
1
3
[
(
a
×
b
)
⋅
c
]
is equal to
[17 Mar 2021 Shift 1]
Your Answer:
Validate
Solution:
a
=
⟨
α
,
β
,
3
⟩
b
=
⟨
−
β
,
−
α
,
−
1
⟩
c
=
⟨
1
,
−
2
,
−
1
⟩
a
⋅
b
=
1
−
α
β
−
α
β
−
3
=
1
α
β
=
−
2
b
⋅
c
=
−
3
−
β
+
2
α
+
1
=
−
3
β
−
2
α
=
4
⇒
β
−
2
(
−
2
β
)
=
4
⇒
β
2
+
4
=
4
β
⇒
β
2
−
4
β
+
4
=
0
⇒
(
β
−
2
)
2
=
0
⇒
β
=
2
α
β
=
−
2
⇒
α
⋅
2
=
−
2
⇒
α
=
−
1
Hence,
1
3
[
(
a
×
b
)
⋅
c
]
a
=
⟨
−
1
,
2
,
3
⟩
b
=
⟨
−
2
,
1
,
−
1
⟩
c
=
⟨
1
,
−
2
,
−
1
⟩
(
a
×
b
)
=
|
∧
i
∧
j
∧
k
−
1
2
3
−
2
1
−
1
|
=
−
5
∧
i
−
7
∧
j
+
3
∧
k
(
a
×
b
)
⋅
c
=
(
−
5
∧
i
−
7
∧
j
+
3
∧
k
)
(
∧
i
−
2
∧
j
−
∧
k
)
=
−
5
+
14
−
3
=
6
∴
1
3
[
(
a
×
b
)
⋅
c
]
=
1
3
×
6
=
2
© examsnet.com
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