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Byju's Answer
Standard XII
Mathematics
Cross Product of Two Vectors
For any three...
Question
For any three vectors
→
a
,
→
b
,
→
c
→
a
×
(
→
b
+
→
c
)
+
→
b
×
(
→
c
+
→
a
)
+
→
c
×
(
→
a
+
→
b
)
equals to
A
→
a
+
→
b
+
→
c
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B
[
→
a
→
b
→
c
]
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C
→
a
×
→
b
×
→
c
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D
0
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Solution
The correct option is
D
0
→
a
×
(
→
a
+
→
c
)
+
→
b
×
(
→
c
+
→
a
)
+
→
c
×
(
→
a
+
→
b
)
expanding by associated property
[
→
a
×
(
→
b
+
→
c
)
=
→
a
×
→
b
+
→
a
×
c
]
[
→
a
×
→
b
+
→
b
×
→
a
]
+
[
→
a
×
→
c
+
→
c
×
→
a
]
+
[
→
b
×
→
c
+
→
c
×
→
b
]
[
∵
→
a
×
→
b
=
−
(
→
b
×
a
)
]
[
∴
(
→
a
×
→
b
+
→
b
×
→
a
)
=
0
]
0
+
0
+
0
=
0
Suggest Corrections
1
Similar questions
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
,
→
c
are three vectors such that
→
a
,
→
b
,
→
c
, then prove that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
, and hence show that
[
→
a
→
b
→
c
]
=
0.
Q.
If
→
a
,
→
b
,
→
c
are three vectors such that
→
a
×
→
b
=
→
c
,
→
b
×
→
c
=
→
a
,
→
c
×
→
a
=
→
b
then prove that
|
→
a
|
=
|
→
b
|
=
|
→
c
|
Q.
If
→
a
,
→
b
,
→
c
are three vectors such that
→
a
+
→
b
+
→
c
=
→
0
,
then prove that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
,
and hence show that
[
→
a
→
b
→
c
]
=
0.
Q.
If
→
a
,
→
b
,
→
c
are three vectors and
|
→
b
|
=
|
→
c
|
then
(
→
a
+
→
b
)
×
(
→
a
+
→
c
)
}
×
(
→
b
×
→
c
)
.
(
→
b
+
→
c
)
=
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