If `a=hati+hatk-2hatk, b=2hati-hatj+hatk and c=3hati-hatk c =ma+nb` then m+n ios equal to

Options

A. 0
B. 1
C. 2
D. `-1`

Answer

C

Explanation

Given `a=hati+hatj-2hatk, b=2hati-hatj+hatk, c=3hati-ghatk` and c=ma+nb
`therefoe 3hati-hatk=m(hati+hatj-2hatk)+n(2hati-hatj+hatk)`
`Rightarrow 3hati-hatk=(m+2n)hati+(m-n)hatj+(-2m+n)hatk`
On equation the coefficient of `hati,hatj and hatk` respectively.
we get
`3=m+2n, 0=m-n`
`and =1=-2m+n`
`Rightarrow 3=n+2n`
`Rightarrow 3=n+2n`
and -1=-2m+n
`Rightarrow 3=n+2n`
`Rightarrow n=1 `
`Rightarrow m=1 and n=1`
`Rightarrow m+n=1+1=2`