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UPSC NDA Math Model Paper 7
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© examsnet.com
Question : 40
Total: 120
If
→
a
+
→
b
+
→
c
=
0
and
|
→
a
|
=
3
,
|
→
b
|
=
4
,
|
→
c
|
=
5
then the angle between
→
a
and
→
b
is :
30°
45°
60°
90°
Validate
Solution:
|
a
|
=
3
,
|
b
|
=
4
,
|
c
|
=
5
a
+
b
+
c
=
0
⟹
a
+
b
=
−
c
⇒
|
a
+
b
|
=
|
−
c
|
⇒
|
a
+
b
|
2
=
|
−
c
|
2
⇒
|
a
|
2
+
|
b
|
2
+
2
a
⋅
b
=
|
c
|
2
⇒
9
+
25
+
2
a
⋅
b
=
49
Also
a
b
=
3
×
5
Hence
9
+
25
+
2
a
b
cos
θ
=
49
⇒
15
=
30
cos
θ
Or
cos
θ
=
1
2
θ
=
60
∘
so angle is
60
∘
.
© examsnet.com
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