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Byju's Answer
Standard XII
Mathematics
Scalar Triple Product
If A,B, C are...
Question
If
→
A
,
→
B
,
→
C
are non-zero vectors. Then the scalar
→
A
⋅
(
→
B
+
→
C
)
×
(
→
A
+
→
B
+
→
C
)
equals to:
A
0
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B
[
→
A
→
B
→
C
]
+
[
→
B
→
C
→
A
]
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C
[
→
A
→
B
→
C
]
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D
None of these
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Solution
The correct option is
A
0
Let
E
=
→
A
⋅
(
→
B
+
→
C
)
×
(
→
A
+
→
B
+
→
C
)
Let
→
a
=
→
A
,
→
b
=
(
→
B
+
→
C
)
and
→
c
=
(
→
A
+
→
B
+
→
C
)
⇒
E
=
→
a
⋅
(
→
b
×
→
c
)
⇒
E
=
[
→
A
→
B
→
C
]
∣
∣ ∣
∣
1
0
0
0
1
1
1
1
1
∣
∣ ∣
∣
⇒
E
=
[
→
A
→
B
→
C
]
×
0
=
0
Suggest Corrections
3
Similar questions
Q.
If
→
a
,
→
b
,
→
c
are non-zero, non-coplanar vectors then
{
→
a
×
(
→
b
+
→
c
)
}
×
{
→
b
×
(
→
c
−
→
a
)
}
is collinear with the vector(s)
Q.
If
→
a
,
→
b
,
→
c
are non coplanar vectors, then
[
→
a
×
→
b
,
→
b
×
→
c
,
→
c
×
→
a
]
is equal to
Q.
If
→
a
,
→
b
,
→
c
are three non coplanar, non zero vectors and
→
r
is any vector in space, then
(
→
a
×
→
b
)
×
(
→
r
×
→
c
)
+
(
→
b
×
→
c
)
×
(
→
r
×
→
a
)
+
(
→
c
×
→
a
)
×
(
→
r
×
→
b
)
is equal to
λ
[
→
a
→
b
→
c
]
. Then the value of
λ
is
Q.
If
→
a
,
→
b
and
→
c
are three non-zero vectors such that
→
a
.
→
b
=
→
a
.
→
c
,
then
Q.
If
→
a
,
→
b
,
→
c
are three non-zero vectors, no two of which are collinear and the vector
→
a
+
→
b
is collinear with
→
c
, and
→
b
+
→
c
is collinear with
→
a
, then
→
a
+
→
b
+
→
c
is equal to
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