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UPSC NDA Math Model Paper 6
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© examsnet.com
Question : 8
Total: 120
For the vectors
→
a
=
−
4
^
i
+
2
^
j
,
→
b
=
2
^
i
+
^
j
and
→
c
=
2
^
i
+
3
^
j
, if
→
c
=
m
^
a
+
n
^
b
, then the value of m + n is:
1
2
3
2
5
2
7
2
Validate
Solution:
We have
→
c
=
m
^
a
+
n
^
b
.
⇒
2
^
i
+
3
^
j
=
m
(
−
4
^
i
+
2
^
j
)
+
n
(
2
^
i
+
^
j
)
⇒
2
^
i
+
3
^
j
=
(
−
4
m
+
2
n
)
^
i
+
(
2
m
+
n
)
^
j
Equating the scalar coefficients, we get:
−
4
m
+
2
n
=
2
... (1)
2
m
+
n
=
3
... (2)
Multiplying equation (2) by 2 and adding to equation (1), we get:
4n = 8
⇒ n = 2
Using either of the equations above, we also get:
m
=
1
2
∴
m
+
n
=
2
+
1
2
=
5
2
.
© examsnet.com
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