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Byju's Answer
Standard XI
Physics
Multiplication with Vectors
If a, b, c be...
Question
If
→
a
,
→
b
,
→
c
be any three non - coplanar vectors, then calculate the value of
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
is
A
2
[
→
a
+
→
b
+
→
c
]
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B
2
[
→
a
→
b
→
c
]
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C
2
√
[
→
a
+
→
b
+
→
c
]
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D
[
→
a
+
→
b
+
→
c
]
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Solution
The correct option is
B
2
[
→
a
→
b
→
c
]
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
(
→
a
+
→
b
)
.
{
(
→
b
+
→
c
)
×
(
→
c
+
→
a
)
}
=
(
→
a
+
→
b
)
.
(
→
b
×
→
c
+
→
b
×
→
a
+
→
c
×
→
c
+
→
c
×
→
a
)
=
(
→
a
+
→
b
)
.
(
→
b
×
→
c
+
→
b
×
→
a
+
→
c
×
→
a
)
=
→
a
(
→
b
×
→
c
)
+
→
a
(
→
b
×
→
a
)
+
→
a
.
(
→
c
×
→
a
)
+
→
b
.
(
→
b
×
→
c
)
+
→
b
(
→
b
×
→
a
)
+
→
b
.
(
→
c
×
→
a
)
=
[
→
a
→
b
→
c
]
+
[
→
b
→
c
→
a
]
=
2
[
→
a
→
b
→
c
]
Suggest Corrections
5
Similar questions
Q.
If
→
a
,
→
b
,
→
c
be any three non - coplanar vectors, then calculate the value of
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
is
Q.
If
→
a
,
→
b
,
→
c
be any three non - coplanar vectors, then calculate the value of
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
is
Q.
If
→
a
,
→
b
,
→
c
be three non-coplanar vectors and
→
r
be any arbitrary vector, then
(
→
a
×
→
b
)
×
(
→
r
×
→
c
)
+
(
→
b
×
→
c
)
×
(
→
r
×
→
a
)
+
(
→
c
×
→
a
)
×
(
→
r
×
→
b
)
is equal to
Q.
Assertion :If
a
,
b
,
c
are three non-coplanar, non-zero vectors, then
(
a
.
a
)
b
×
c
+
(
a
.
b
)
c
×
a
+
(
a
.
c
)
a
×
b
=
[
b
c
a
]
a
Reason: If the vectors
a
,
b
,
c
are non-coplanar, then so are
b
×
c
,
c
×
a
,
a
×
b
Q.
If
A
,
B
,
C
are three non-coplanar vectors, then find the value of
A
⋅
(
B
×
C
)
(
C
×
A
)
⋅
B
+
B
⋅
(
A
×
C
)
C
⋅
(
A
×
B
)
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