If ` vec a=i+j ,\ vec b=j+k\ a n d\ vec c=k+i ,\ ` write unit vectors parallel to ` vec a+ vec b-2 vec c dot`

Explanation

Let `vecr= vec a+ vec b-2 vec c`

`=hati+hatj+hatj+hatk-2(hatk+hati)`

`=-hati+2hatj-hatk`

Unit vector parallel to `vec r` is the required vector,

`={-hati+2hatj-hatk}/sqrt{(-1)^2+2^2+(-1)^2}`

`={-hati+2hatj-hatk}/2`

`=-1/2hati+hatj-1/2hatk`