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KEAM 2019 Math Paper
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© examsnet.com
Question : 29
Total: 121
If
a
and
b
are unit vectors and
θ
is the angle between them, then
|
a
−
b
2
|
is
sin
2
θ
sin
θ
sin
θ
2
2
sin
2
θ
0
Validate
Solution:
a
⋅
b
=
|
a
|
|
b
|
cos
θ
=
1
⋅
cos
θ
=
cos
θ
|
a
−
b
2
|
2
=
(
a
−
b
)
⋅
(
a
−
b
)
4
=
|
a
|
2
+
|
b
|
2
−
2
a
⋅
b
4
=
1
+
1
−
2
a
⋅
b
4
=
2
−
2
|
a
|
|
b
|
cos
θ
4
|
a
−
b
2
|
=
sin
(
θ
2
)
© examsnet.com
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