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NIMCET 2008 Question Paper with solutions
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© examsnet.com
Question : 32
Total: 120
If
A
+
B
+
C
=
0
,
|
A
|
=
3
,
|
B
|
=
5
,
|
C
|
=
7
,
then the angle between
A
and
B
is
π
6
2
π
3
5
π
3
π
4
Validate
Solution:
Given,
A
+
B
+
C
=
0
⇒
−
C
=
(
A
+
B
)
⇒
(
−
C
)
⋅
(
−
C
)
=
(
A
+
B
)
⋅
(
A
+
B
)
⇒
|
C
|
2
=
|
A
|
2
+
|
B
|
2
+
2
(
A
⋅
B
)
⇒
|
C
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
⋅
cos
θ
⇒
49
=
25
+
9
+
2
(
3
×
5
cos
θ
)
where 0 is the angle between
A
and
B
.
⇒
cos
θ
=
1
2
⇒
θ
=
π
3
or
2
π
−
π
3
=
5
π
3
© examsnet.com
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