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Byju's Answer
Standard XII
Mathematics
Collinear Vectors
If [ a + b b...
Question
If
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
λ
1
[
→
a
→
b
→
c
]
and
[
→
a
×
→
b
→
b
×
→
c
→
c
×
→
a
]
=
[
→
a
→
b
→
c
]
λ
2
then
λ
1
+
λ
2
3
is (where
→
a
,
→
b
,
→
c
are non zero and non coplanar vectors)
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Solution
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
(
→
a
+
→
b
)
.
(
(
→
b
+
→
c
)
×
(
→
c
+
→
a
)
)
=
(
→
a
+
→
b
)
.
(
→
b
×
→
c
+
→
b
×
→
a
+
→
c
×
→
a
)
=
[
→
a
→
b
→
c
]
+
[
→
b
→
c
→
a
]
=
2
[
→
a
→
b
→
c
]
[
→
a
×
→
b
→
b
×
→
c
→
c
×
→
a
]
=
(
→
a
×
→
b
)
.
(
(
→
b
×
→
c
)
×
(
→
c
×
→
a
)
)
=
(
→
a
×
→
b
)
.
[
→
b
→
c
→
a
]
→
c
=
[
→
a
→
b
→
c
]
2
λ
1
=
2
,
λ
2
=
2
λ
1
+
λ
2
3
=
1.33
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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, 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
Q.
If
→
a
,
→
b
,
→
c
are three non-coplanar non-zero vectors and
→
r
is any vector, then
(
→
a
×
→
b
)
×
(
→
r
×
→
c
)
+
(
→
b
×
→
c
)
×
(
→
r
×
→
a
)
+
(
→
c
×
→
a
)
×
(
→
r
×
→
b
)
=
Q.
If
→
a
,
→
b
,
→
c
are three non coplanar non zero vectors, then
(
→
a
⋅
→
a
)
→
b
×
→
c
+
(
→
a
⋅
→
b
)
→
c
×
→
a
+
(
→
a
.
→
c
)
→
a
×
→
b
is equal to
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