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Byju's Answer
Standard XII
Mathematics
Binomial Coefficients
If a⃗, b⃗, ...
Question
If
→
a
,
→
b
,
→
c
are non-coplanar non-zero vectors such that
→
b
×
→
c
=
→
a
,
→
a
×
→
b
=
→
c
,
→
c
×
→
a
=
→
b
, then
A
|
→
a
|
=
1
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B
|
→
b
|
=
1
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C
|
→
a
|
+
|
→
b
|
+
|
→
c
|
=
3
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N
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e
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h
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s
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Solution
The correct options are
A
|
→
a
|
=
1
B
|
→
b
|
=
1
C
|
→
a
|
+
|
→
b
|
+
|
→
c
|
=
3
We have
→
b
×
→
c
=
→
a
⇒
[
→
a
→
b
→
c
]
=
(
→
a
.
→
a
)
=
|
→
a
|
2
Similarly
[
→
a
→
b
→
c
]
=
|
→
b
|
2
=
|
→
c
|
2
∴
|
→
a
|
=
|
→
b
|
=
|
→
c
|
=
√
[
→
a
→
b
→
c
]
Now ,
[
→
b
×
→
c
→
c
×
→
a
→
a
×
→
b
]
=
[
→
a
→
b
→
c
]
2
∴
[
→
a
→
b
→
c
]
=
[
→
a
→
b
→
c
]
2
(from the question)
But
[
→
a
→
b
→
c
]
≠
0.
So
[
→
a
→
b
→
c
]
=
1.
Hence,
|
→
a
|
=
|
→
b
|
=
|
→
c
|
=
1.
Suggest Corrections
0
Similar questions
Q.
If
→
a
,
→
b
,
→
c
are non coplanar non zero vectors, then the value of
(
→
a
×
→
b
)
×
(
→
a
×
→
c
)
+
(
→
b
×
→
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)
×
(
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×
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)
+
(
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×
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×
(
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×
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is
Q.
If
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,
→
b
,
→
c
are non coplanar vectors such that
→
b
×
→
c
=
→
a
,
→
c
×
→
a
=
→
b
and
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×
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, then
Q.
If
→
a
,
→
b
,
→
c
are non-zero non-collinear vectors such that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
, then
→
a
+
→
b
+
→
c
=
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 non-coplanar vectors, then
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→
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×
→
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→
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×
→
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→
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]
=
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