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Byju's Answer
Standard XII
Mathematics
Collinear Vectors
If a⃗, b⃗, c⃗...
Question
If
→
a
,
→
b
,
→
c
are three vectors such that
[
→
a
→
b
→
c
]
=
5
, then the value of
[
→
a
×
→
b
,
→
b
×
→
c
,
→
c
×
→
a
]
is _______
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Solution
Given,
[
→
a
→
b
→
c
]
=
5
We know that,
[
→
a
×
→
b
,
→
b
×
→
c
,
→
c
×
→
a
]
=
[
→
a
→
b
→
c
]
2
=
5
2
=
25
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Similar questions
Q.
If
→
a
,
→
b
,
→
c
are vectors such that
[
→
a
→
b
→
c
]
=
4
then
[
→
a
×
→
b
→
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×
→
c
→
c
×
→
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]
=
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Q.
If
→
a
,
→
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,
→
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
=
→
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 such that
→
a
×
→
b
=
→
c
,
→
b
×
→
c
=
→
a
,
→
c
×
→
a
=
→
b
then prove that
|
→
a
|
=
|
→
b
|
=
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→
c
|
Q.
If
→
a
,
→
b
and
→
c
are three non-coplanar vectors, then
(
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a
+
→
b
+
→
c
)
⋅
[
(
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+
→
b
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×
(
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+
→
c
)
]
equals
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