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Byju's Answer
Standard XII
Mathematics
Addition of Vectors
If a⃗,b⃗, c...
Question
If
→
a
,
→
b
,
→
c
are non-zero non-collinear vectors such that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
, then
→
a
+
→
b
+
→
c
=
A
a
b
c
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B
−
1
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C
→
0
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D
2
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Solution
The correct option is
B
→
0
→
a
×
→
b
=
→
b
×
→
c
(
→
a
+
→
c
)
×
→
b
=
o
(
→
a
+
→
c
+
→
b
)
×
→
b
=
→
b
×
→
b
(
→
a
+
→
c
+
→
b
)
×
→
b
=
0
→
a
+
→
c
+
→
b
=
→
0
hence
→
a
,
→
b
,
→
c
are non collinear
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0
Similar questions
Q.
If
→
a
,
→
b
,
→
c
are non-coplanar non-zero vectors such that
→
b
×
→
c
=
→
a
,
→
a
×
→
b
=
→
c
,
→
c
×
→
a
=
→
b
, then
Q.
If
→
a
,
→
b
,
→
c
are non-zero vectors such that
|
(
→
a
×
→
b
)
.
→
c
|
=
|
→
a
|
|
→
b
|
|
→
c
|
, then
|
→
a
+
→
b
+
→
c
|
2
=
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 non-zero, non-coplanar vectors then
{
→
a
×
(
→
b
+
→
c
)
}
×
{
→
b
×
(
→
c
−
→
a
)
}
is collinear with the vector
Q.
If
→
a
,
→
b
,
→
c
are non coplanar non zero vectors, then the value of
(
→
a
×
→
b
)
×
(
→
a
×
→
c
)
+
(
→
b
×
→
c
)
×
(
→
b
×
→
a
)
+
(
→
c
×
→
a
)
×
(
→
c
×
→
b
)
is
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