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AP EAMCET Engineering 17 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 3
Total: 160
If
→
a
+
→
b
+
→
c
=
→
0
and
|
→
a
|
=
3
,
|
→
b
|
=
5
,
|
→
c
|
=
7
,
then the angle between
→
a
and
→
b
is
30
°
120
°
90
°
60
°
Validate
Solution:
Given,
a
+
b
+
c
=
0
⇒
(
a
+
b
)
=
−
c
⇒
(
a
+
b
)
2
=
c
2
⇒
a
2
+
b
2
+
2
a
⋅
b
=
c
2
⇒
2
a
⋅
b
=
c
2
−
a
2
−
b
2
As square of a vector
=
square of its magnitude,
⇒
2
a
⋅
b
=
49
−
9
−
25
⇒
2
a
⋅
b
cos
θ
=
15
⇒
cos
θ
=
15
2
×
3
×
5
θ
=
cos
−
1
(
1
2
)
=
60
∘
© examsnet.com
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