If `a=hat(i)+hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k)` and `c=3hat(i)-hat(k)` and `c=ma+nb`, then `m+n` is 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 and c=m +a+nb`
`therefore 3hati-hatk=m(hati+hatj-2hatk)+n(2hati-hatj+hatk)`
`implies3hati-hatk=(m+2n)hati+(m-n)hatj+(-2m+n)hatk`
On equationg the coefficients of `hati,hatj and hatk,` respectively, we get
`3=m+2n,0=m-n`
`and -1=-2m+n`
`implies3=n+2n`
`impliesn=1`
`impliesm=1and n=1`
` impliesm+n=1+1=2`