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UPSC NDA Math Model Paper 10
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© examsnet.com
Question : 97
Total: 120
Let
|
→
a
|
≠
0
,
|
→
b
|
≠
0
(
→
a
+
→
b
)
.
(
→
a
+
→
b
)
=
|
→
a
|
2
+
|
→
b
|
2
Holds if and only if
→
a
and
→
b
are perpendicular
→
a
and
→
b
are parallel
→
a
and
→
b
are inclined at an angle of
45
°
→
a
and
→
b
are anti-parallel
Validate
Solution:
Given:
(
→
a
+
→
b
)
.
(
→
a
+
→
b
)
=
|
→
a
|
2
+
|
→
b
|
2
=
|
→
a
|
2
+
|
→
b
|
2
+
2
→
a
.
→
b
=
|
→
a
|
2
+
|
→
b
|
2
⇒
2
→
a
.
→
b
=
0
⇒
→
a
.
→
b
=
0
∴
→
a
and
→
b
are perpendicular.
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