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Byju's Answer
Standard XII
Mathematics
Logarithmic Differentiation
[ a⃗ +b⃗ b⃗ +...
Question
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
[
→
a
→
b
→
c
]
, then
A
[
→
a
→
b
→
c
]
=
1
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B
→
a
,
→
b
,
→
c
are coplanar
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C
[
→
a
→
b
→
c
]
=
−
1
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D
→
a
,
→
b
,
→
c
are mutually perpendicular
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Solution
The correct option is
C
→
a
,
→
b
,
→
c
are coplanar
Given,
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
[
→
a
→
b
→
c
]
[
a
⃗
+
b
⃗
b
⃗
+
c
⃗
c
⃗
+
a
⃗
]
=
[
a
⃗
b
⃗
c
⃗
]
are coplanar.
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Similar questions
Q.
If
→
a
,
→
b
and
→
c
are three non-coplanar vectors, then
(
→
a
+
→
b
+
→
c
)
⋅
[
(
→
a
+
→
b
)
×
(
→
a
+
→
c
)
]
equals
Q.
Prove that for any three vectors
→
a
,
→
b
and
→
c
,
[
(
→
a
+
→
b
)
(
→
b
+
→
c
)
(
→
c
+
→
a
)
]
=
2
[
→
a
→
b
→
c
]
.
Q.
If
→
a
,
→
b
,
→
c
are three non coplanar vectors,
→
p
=
→
b
×
→
c
[
→
a
→
b
→
c
]
,
→
q
=
→
c
×
→
a
[
→
a
→
b
→
c
]
,
→
r
=
→
a
×
→
b
[
→
a
→
b
→
c
]
, then
(
2
→
a
+
3
→
b
+
4
→
c
)
.
→
p
+
(
2
→
b
+
3
→
c
+
4
→
a
)
.
→
q
+
(
2
→
c
+
3
→
a
+
4
→
b
)
.
→
r
=
Q.
If
→
a
,
→
b
,
→
c
are vectors such that
[
→
a
→
b
→
c
]
=
4
then
[
→
a
×
→
b
→
b
×
→
c
→
c
×
→
a
]
=
?
Q.
If
→
a
,
→
b
and
→
c
are three non-coplanar vectors, then
(
→
a
+
→
b
+
→
c
)
⋅
[
(
→
a
+
→
b
)
×
(
→
a
+
→
c
)
]
equals
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