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Byju's Answer
Standard XII
Physics
Work Done as Dot Product
If 4 a⃗ +5 ...
Question
If
4
→
a
+
5
→
b
+
9
→
c
=
0
, then
(
→
a
×
→
b
)
×
[
(
→
b
×
→
c
)
×
(
→
c
×
→
a
)
]
is equal to
A
a vector perpendicular to the plane of
→
a
,
→
b
and
→
c
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B
a scalar quantity
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C
0
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D
Vector quantity
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Solution
The correct option is
B
0
Let,
4
→
a
+
5
→
b
+
9
→
c
=
0
......(1).
Now,
(
→
a
×
→
b
)
×
[
(
→
b
×
→
c
)
×
(
→
c
×
→
a
)
]
=
(
→
a
×
→
b
)
×
[
{
(
→
b
×
→
c
)
.
→
a
}
→
c
−
{
(
→
b
×
→
c
)
.
→
c
}
→
a
]
.
=
(
→
a
×
→
b
)
×
[
→
b
→
c
→
a
]
→
c
[Since,
[
→
b
→
c
→
c
]
=
0
]
=
→
0
.
As,
[
→
b
→
c
→
a
]
=
[
→
a
→
b
→
c
]
=
(
→
a
×
→
b
)
.
(
−
4
9
→
a
−
5
9
→
b
)
[Using (1)]
=
−
4
9
[
→
a
→
b
→
a
]
−
5
9
[
→
a
→
b
→
b
]
=
0
.
Suggest Corrections
0
Similar questions
Q.
For any three vectors
→
a
,
→
b
,
→
c
→
a
×
(
→
b
+
→
c
)
+
→
b
×
(
→
c
+
→
a
)
+
→
c
×
(
→
a
+
→
b
)
equals to
Q.
Let
→
A
=
→
b
×
→
c
,
→
B
=
→
c
×
→
a
,
→
C
=
→
a
×
→
b
, then the vectors
→
A
×
(
→
B
×
→
C
)
,
→
B
×
(
→
C
×
→
A
)
, and
→
C
×
(
→
A
×
→
B
)
are
Q.
If
→
a
,
→
b
and
→
c
are unit vectors satisfying
|
→
a
−
→
b
|
2
+
|
→
b
−
→
c
|
2
+
|
→
c
−
→
a
|
2
=
9
, then
|
2
→
a
+
5
→
b
+
5
→
c
|
is
Q.
Let
→
a
,
→
b
and
→
c
be three vectors such that
|
→
a
|
=
√
3
,
|
→
b
|
=
5
,
→
b
.
→
c
=
10
and the angle between
→
b
and
→
c
is
π
3
.
If
→
a
is perpendicular to vector
→
b
×
→
c
, then
|
→
a
×
(
→
b
×
→
c
)
|
is equal to
Q.
If
→
a
+
→
b
+
→
c
=
0
, the prove that:
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
where
→
a
,
→
b
,
→
c
are non-zero vectors.
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