First we write it as a difference of vectors, 
but not necessarily unit vectors.

⟨-7-(-1),5-3,1-(-2)⟩ =

⟨-7+1,2,1+2⟩ =

⟨-6,2,3⟩ =

-6i + 2j + 3k

Now that is a sum of scalar multiples of unit vectors

i, j, and k

I have no idea why you would want to write that as

a sum of unit vectors.  But since that's what you say

you want, since i, j, and k are unit vectors, we could

write -6i + 2j + 3k

as this sum of unit vectors:

-i-i-i-i-i-i+j+j+k+k+k

but that is very silly.  Are you sure that's what

you were asked to do?  

Edwin