MHTCET 2016 Math Solved Paper

(c) Given,

→

a

=

^

i

+

^

j

−2

^

k

,

→

b

= 2

^

i

−

^

j

+

^

k

,

→

c

=3

^

i

−

^

k

and

→

c

=m

→

a

+n

→

b

As, 3

^

i

−

^

k

= m(

^

i

+

^

j

−2

^

k

) + n(2

^

i

−

^

j

+

^

k

)
⇒3

^

i

−

^

k

= (m+2n)

^

i

+ (m−n)

^

j

+ (−2m+n)

^

k

After equating the coefficient of

^

i

,

^

j

and

^

k

, on both sides respectively, we get
3 = m + 2n, 0 = m - n and -1 = - 2 m + n
⇒ 3 = n + 2n ⇒ n = 1
⇒ m = 1 and n = 1
⇒ m + n = 1+ 1 = 2