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Byju's Answer
Standard XII
Mathematics
Intersection
If a⃗ ,b⃗ ,...
Question
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.
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Solution
Given
→
a
,
→
b
,
→
c
are three vectors such that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
Consider
→
a
×
→
b
=
→
b
×
→
c
,
⟹
(
→
a
×
→
b
)
.
→
c
=
(
→
b
×
→
c
)
.
→
c
⟹
[
→
a
→
b
→
c
]
=
[
→
b
→
c
→
c
]
=
0
similarly
[
→
b
→
c
→
a
]
and
[
→
c
→
a
→
b
]
are zeros
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Similar questions
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
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a
,
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,
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×
→
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=
→
c
,
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b
×
→
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=
→
a
,
→
c
×
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=
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then prove that
|
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|
=
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Q.
If
→
a
,
→
b
,
→
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are vectors such that
[
→
a
→
b
→
c
]
=
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then
[
→
a
×
→
b
→
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×
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a
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=
?
Q.
If
→
A
,
→
B
&
→
C
are vectors such that
|
→
B
|
=
|
→
C
|
, Prove that :
[
(
→
A
+
→
B
)
×
(
→
A
+
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C
)
]
×
(
→
B
×
→
C
)
.
(
→
B
+
→
C
)
=
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Q.
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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