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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
If e⃗1 ...
Question
If
→
e
1
&
→
e
2
are two unit vectors and
θ
is the angle between them, then
sin
(
θ
2
)
is
A
1
2
|
→
e
1
+
→
e
2
|
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B
1
2
|
→
e
1
−
→
e
2
|
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C
→
e
1
.
→
e
2
2
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D
|
→
e
1
×
→
e
2
|
2
|
→
e
1
|
|
→
e
2
|
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Solution
The correct option is
B
1
2
|
→
e
1
−
→
e
2
|
sin
(
θ
2
)
=
1
2
√
4
sin
2
θ
2
=
1
2
√
2
(
1
−
cos
θ
)
=
1
2
√
1
+
1
−
2.
cos
θ
=
1
2
√
→
e
1
2
+
→
e
2
2
−
2
|
→
e
1
|
|
→
e
2
|
cos
θ
=
1
2
√
(
→
e
1
−
→
e
2
)
2
=
1
2
|
→
e
1
−
→
e
2
|
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