If `veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -hatk , " then " vecb` is

Options

A. `hati-hatj+hatk`
B. `2hatj-hatk`
C. `hati`
D. `2hati`

Answer

C

Explanation

Given that ` a= hati + hatj + hatk , a.b =1`
`and axxb= hatj = hatk`
As , we know ` a xx (axxb)=(a.b)a-(a.a)b`
`implies ( hati + hatj + hatk ) xx(hatj - hatk ) = ( hati + hatj + hatk)-3b`
`[ :' a.a =1+1+1=3]`
`implies - 2 hati + hatj + hatk = hati + hatj + hatk -3b`
`implies 3b=3 hati`
`implies b= hati`