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Byju's Answer
Standard XII
Mathematics
Linear Combination of Vectors
If a,b are tw...
Question
If
→
a
,
→
b
are two vectors such that
|
→
a
×
→
b
|
=
2
,
then the value of
[
→
a
→
b
→
a
×
→
b
]
is
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Solution
We know
[
→
P
→
Q
→
R
]
=
[
→
Q
→
R
→
P
]
=
[
→
R
→
P
→
Q
]
Therefore,
[
→
a
→
b
→
a
×
→
b
]
=
(
→
a
×
→
b
)
⋅
(
→
a
×
→
b
)
=
|
→
a
×
→
b
|
2
=
4
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Similar questions
Q.
If
→
a
and
→
b
are two non zero vectors such that
→
a
×
→
b
=
→
b
×
→
a
,
then
Q.
For any three vectors
→
a
,
→
b
and
→
c
, prove that vectors
→
a
−
→
b
,
→
b
−
→
c
and
→
c
−
→
a
are coplanar.
Q.
If
→
a
,
→
b
and
→
c
are three non-coplanar vectors and
→
p
,
→
q
and
→
r
are vectors defined by
→
p
=
→
b
×
→
c
[
→
a
→
b
→
c
]
,
→
q
=
→
c
×
→
a
[
→
a
→
b
→
c
]
and
→
r
=
→
a
×
→
b
[
→
a
→
b
→
c
]
, then the value of
(
→
a
+
→
b
)
⋅
→
p
+
(
→
b
+
→
c
)
⋅
→
q
+
(
→
c
+
→
a
)
⋅
→
r
=
Q.
If
→
a
,
→
b
,
→
c
are non - coplanar vectors, then
a
.
(
b
×
c
)
(
c
×
a
)
.
b
+
b
.
(
a
×
c
)
c
.
(
a
×
b
)
=
?
Q.
If
→
a
,
→
b
,
→
c
,
→
d
are non-zero vectors, then
[
→
a
×
→
b
→
a
×
→
c
→
d
]
can be simplified as:
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Linear Combination of Vectors
Standard XII Mathematics
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