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Byju's Answer
Standard XII
Mathematics
Definition of Vector
Let a , b a...
Question
Let
→
a
,
→
b
a
n
d
→
c
be three unit vectors such that
→
a
x
(
→
b
x
→
c
)
=
√
3
2
(
→
b
+
→
c
)
. If
→
b
is not parallel to
→
c
,
then the angle between
→
a
and
→
b
is :
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Solution
→
a
×
(
→
b
×
→
c
)
=
√
3
2
(
→
b
+
→
c
)
(
→
a
.
→
c
)
→
b
−
(
→
a
.
→
b
)
→
c
=
√
3
2
(
→
b
+
→
c
)
C
o
m
p
a
r
i
n
g
,
→
a
.
→
b
=
−
√
3
2
|
→
a
|
∣
∣
→
b
∣
∣
cos
θ
=
−
√
3
2
A
n
g
l
e
b
e
t
w
e
e
n
→
a
a
n
d
→
b
i
s
θ
=
150
0
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Similar questions
Q.
Let
→
a
,
→
b
and
→
c
be three unit vectors such that
→
a
×
(
→
b
×
→
c
)
=
√
3
2
(
→
b
+
→
c
)
. If
→
b
is not parallel to
→
c
, then the angle between
→
a
and
→
b
is:
Q.
If
→
a
,
→
b
and
→
c
are three coplanar unit vectors such that
→
a
×
(
→
b
×
→
c
)
=
→
b
2
, then the angle between
→
b
and
→
c
can be
Q.
Let
→
a
,
→
b
,
→
c
be nonzero vectors such that
(
→
a
×
→
b
)
×
→
c
=
1
3
∣
∣
∣
→
b
∣
∣
∣
∣
∣
→
c
∣
∣
→
a
. If
θ
is the angle between
→
b
and
→
c
, then
sin
θ
=
Q.
Let
→
a
,
→
b
and
→
c
be three non-zero vectors such that no two of them are collinear and
(
→
a
×
→
b
)
×
→
c
=
1
3
∣
∣
∣
→
b
∣
∣
∣
∣
∣
→
c
∣
∣
→
a
. If
θ
is the angle between vectors
→
b
and
→
c
, then a value of
sin
θ
is
Q.
Let
→
a
,
→
b
,
→
c
be unit vectors such that
→
a
is perpendicular to the plane of
→
b
and
→
c
.If the angle between
→
b
and
→
c
is
π
3
, then
∣
∣
∣
→
a
×
→
b
−
→
a
×
→
c
∣
∣
∣
=
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