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Byju's Answer
Standard XII
Mathematics
Algebra of Limits
If αa⃗+βb⃗+...
Question
If
α
→
a
+
β
→
b
+
γ
→
c
=
→
0
, then
(
→
a
×
→
b
)
×
{
(
→
b
×
→
c
)
×
(
→
c
×
→
a
}
=
A
→
0
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B
Avector perpendicular to the plane of
→
a
,
→
b
,
→
c
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C
A scalar quantity
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D
2
[
→
a
→
b
→
c
]
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Solution
The correct option is
A
→
0
Solving
=
→
a
×
→
b
×
(
(
→
b
×
→
c
⋅
→
a
)
→
c
−
(
→
a
×
→
c
⋅
→
c
)
→
a
)
=
→
a
×
→
b
×
→
c
(
→
b
×
→
c
⋅
→
a
)
=
(
(
→
a
−
→
c
)
→
b
−
(
→
a
−
→
b
)
→
c
)
[
→
a
→
b
→
c
]
-----(1)
Now
α
→
a
+
β
→
b
+
γ
→
c
=
→
0
=
α
→
a
×
→
c
+
β
→
b
×
→
c
=
→
0
=
β
→
b
×
→
c
⋅
→
a
=
→
0
[
→
b
→
c
→
a
]
=
0
-----(2)
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0
Similar questions
Q.
If
α
(
→
a
×
→
b
)
+
β
(
→
b
×
→
c
)
+
γ
(
→
c
×
→
a
)
=
→
0
and at least one of the scalars
α
,
β
,
γ
is non-zero, then the vectors
→
a
,
→
b
,
→
c
are
Q.
→
a
≠
→
0
,
→
b
≠
→
0
,
→
a
×
→
b
=
→
0
,
→
c
×
→
b
=
→
0
⇒
→
a
×
→
c
=
Q.
If
→
a
+
→
b
+
→
c
=
→
0
show that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
.
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
and
(
→
a
,
→
b
)
=
π
3
then
|
→
a
×
→
b
|
+
|
→
b
×
→
c
|
+
|
→
c
×
→
a
|
=
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
and
(
→
a
,
→
b
)
=
π
3
, then
∣
∣
→
a
×
→
b
∣
∣
+
∣
∣
→
b
×
→
c
∣
∣
+
|
→
c
×
→
a
|
=
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