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EAMCET Engineering 2010 Solved Paper
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© examsnet.com
Question : 2
Total: 160
If three unit vectors
→
a
,
→
b
,
→
c
satisfy
→
a
+
→
b
+
→
c
=
→
0
, then the angle between
→
a
and
→
b
is
2
π
3
5
π
6
π
3
π
6
Validate
Solution:
Given, condition is
→
a
+
→
b
+
→
c
=
→
0
. . . (i)
and
→
a
,
→
b
,
→
c
are the unit vectors.
Then
|
→
a
|
=
|
→
b
|
=
|
→
c
|
=
1
Let the angle between
→
a
and
→
b
is
θ
.
Now, from Eq. (i)
→
a
+
→
b
+
→
c
=
0
(
→
a
+
→
b
)
=
−
→
c
Squaring on both sides
(
→
a
+
→
b
)
2
=
(
→
c
)
2
[
∵
(
→
c
)
2
=
|
→
c
|
2
]
⇒
(
→
a
)
2
+
(
→
b
)
2
+
2
(
→
a
)
⋅
(
→
b
)
=
|
→
c
|
2
⇒
|
→
a
|
2
+
|
→
b
|
2
+
2
→
a
⋅
→
b
=
|
→
c
|
2
⇒
1
+
1
+
2
{
|
→
a
|
|
→
b
|
cos
θ
}
=
1
[
∵
→
a
⋅
→
b
=
|
→
a
|
|
→
b
|
cos
θ
]
⇒
2
{
1
⋅
1
⋅
cos
θ
}
=
−
1
⇒
cos
θ
=
−
1
2
⇒
cos
θ
=
cos
(
2
π
3
)
⇒
θ
=
2
π
3
© examsnet.com
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