UPSC NDA Math Model Paper 6

We have

→

c

=m

^

a

+n

^

b

.
⇒ 2

^

i

+3

^

j

=m(−4

^

i

+2

^

j

) +n(2

^

i

+

^

j

)
⇒ 2

^

i

+3

^

j

=(−4m+2n)

^

i

+(2m+n)

^

j

Equating the scalar coefficients, we get:
−4m+2n=2 ... (1)
2m+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

.