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Byju's Answer
Standard XII
Mathematics
Strictly Increasing Functions
If a⃗×b⃗=b⃗...
Question
If
→
a
×
→
b
=
→
b
×
→
c
≠
0
, then show that
→
a
+
→
c
=
m
→
b
, where
m
is any scalar.
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Solution
→
a
×
→
b
=
→
b
×
→
c
→
a
×
→
b
−
→
b
×
→
c
=
0
→
a
×
→
b
+
→
c
×
→
b
=
0
(
→
a
+
→
c
)
×
→
b
=
0
→
a
+
→
c
a
n
d
→
b
→
a
+
→
c
=
m
→
b
for angular
m
proved
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0
Similar questions
Q.
If
→
a
×
→
b
=
→
b
×
→
c
≠
→
0
w
i
t
h
→
a
≠
−
→
c
then show that
→
a
+
→
c
=
k
→
b
,
where k is scalar.
Q.
Statement-I :
→
a
×
(
→
b
×
→
c
)
,
→
b
×
(
→
c
×
→
a
)
,
→
c
×
(
→
a
×
→
b
)
are coplanar vectors.
Statement-II: If there exists scalars
l
,
m
,
n
not all zero such that
l
→
a
+
m
→
b
+
n
→
c
=
→
0
, then the vectors
→
a
,
→
b
,
→
c
are coplanar
Q.
If
(
→
a
×
→
b
)
×
→
c
=
→
a
×
(
→
b
×
→
c
)
where
→
a
,
→
b
and
→
c
are any three vectors such that
→
a
.
→
b
≠
0
,
→
b
.
→
c
≠
0
then
→
a
and
→
c
are
Q.
The scalars l and m such that
l
→
a
+
m
→
b
=
→
c
where
→
a
,
→
b
and
→
c
are given vectors, are equal to
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.
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