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Byju's Answer
Standard XII
Mathematics
Angle between Two Line Segments
If e1 and ...
Question
If
e
1
and
e
2
the two unit vectors
θ
is the angle between them, then prove that
s
i
n
(
θ
2
)
is
1
2
|
e
1
−
e
2
|
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Solution
|
A
−
B
|
=
√
(
|
A
|
²
+
|
B
|
²
−
2
|
A
|
|
B
|
.
c
o
s
θ
)
|
e
1
−
e
2
|
=
√
(
|
e
1
|
²
+
|
e
2
|
²
−
2
|
e
1
|
.
|
e
2
|
c
o
s
θ
)
here,
e
1
and
e
2
unit vectors
so,
|
e
1
|
=
1
,
|
e
2
|
=
1
|
e
1
−
e
2
|
=
√
(
1
²
+
1
²
−
2.1.1
c
o
s
θ
)
=
√
(
2
−
2
c
o
s
θ
)
=
√
2
(
1
−
c
o
s
θ
)
=
√
2
∗
2
s
i
n
²
θ
2
=
2
s
i
n
θ
2
hence,
|
e
1
−
e
2
|
=
2
s
i
n
θ
2
s
i
n
θ
2
=
1
2
|
e
1
−
e
2
|
hence proved.
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Similar questions
Q.
Let
e
1
and
e
2
be unit vectors containing angle
θ
. If
1
2
|
e
1
−
e
2
|
=
sin
λ
θ
, then find
λ
.
Q.
let e1 and e2 be unit vectors containing angle x.
then,
1/2[e1-e2]=sinkx
Q.
If
→
e
1
and
→
e
2
are unit vectors and
θ
is the angle between them, then
|
→
e
1
−
→
e
2
|
is equal to :
Q.
If the unit vectors
→
e
1
and
→
e
2
are inclined at an angle
2
θ
and
|
→
e
1
−
→
e
2
|
<
1
, then for
θ
∈
[
0
,
π
]
,
θ
may be in the interval :
Q.
If
→
e
1
=
(
1
,
1
,
1
)
and
→
e
2
=
(
1
,
1
,
−
1
)
and
→
a
and
→
b
are two vectors such that
→
e
1
=
2
→
a
+
→
b
and
→
e
2
=
→
a
+
2
→
b
, then the angle between
→
a
and
→
b
is
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